diff --git a/src/decorations/functions.jl b/src/decorations/functions.jl
index b45cbf15b..c6cf10b8e 100644
--- a/src/decorations/functions.jl
+++ b/src/decorations/functions.jl
@@ -27,7 +27,7 @@ bool_functions = (
 )
 
 bool_binary_functions = (
-    :<, :>, :!=, :⊆, :<=,
+    :<, :>, :!=, :⊆, :<=, :(==),
     :isinterior, :isdisjoint, :precedes, :strictprecedes
 )
 
@@ -36,18 +36,15 @@ for f in bool_functions
 end
 
 for f in bool_binary_functions
-    @eval $(f)(xx::DecoratedInterval, yy::DecoratedInterval) =
+    @eval function $(f)(xx::DecoratedInterval, yy::DecoratedInterval)
+        (isnai(xx) || isnai(yy)) && return false
         $(f)(interval(xx), interval(yy))
+    end
 end
 
 in(x::T, a::DecoratedInterval) where T<:Real = in(x, interval(a))
 
 
-function ==(x::DecoratedInterval, y::DecoratedInterval)
-    isnai(x) && isnai(y) && return true
-    return (==(interval(x), interval(y)))
-end
-
 ## scalar functions: mig, mag and friends
 scalar_functions = (
     :mig, :mag, :inf, :sup, :mid, :diam, :radius, :dist, :eps
diff --git a/test/ITF1788_tests/ieee1788-constructors.jl b/test/ITF1788_tests/ieee1788-constructors.jl
index aeaec40b9..aedb8bc61 100644
--- a/test/ITF1788_tests/ieee1788-constructors.jl
+++ b/test/ITF1788_tests/ieee1788-constructors.jl
@@ -62,7 +62,7 @@ end
 
 # Example from Section 11.3
 @testset "IEEE1788.e" begin
-    @test DecoratedInterval(2, 1) == nai()
+    @test isnai(DecoratedInterval(2, 1))
 end
 
 # Examples from Table 12.1
@@ -99,7 +99,7 @@ end
     @test decoration(@decorated("-10??u")) == decoration(DecoratedInterval(Interval(-10.0, Inf), dac))
     @test @decorated("-10??") == DecoratedInterval(Interval(-Inf, Inf), dac)
     @test decoration(@decorated("-10??")) == decoration(DecoratedInterval(Interval(-Inf, Inf), dac))
-    @test @decorated("[nai]") == nai()
+    @test isnai(@decorated("[nai]"))
     @test @decorated("3.56?1_def") == DecoratedInterval(Interval(0x3.8ccccccccccccp+0, 0x3.91eb851eb8520p+0), def)
     @test decoration(@decorated("3.56?1_def")) == decoration(DecoratedInterval(Interval(0x3.8ccccccccccccp+0, 0x3.91eb851eb8520p+0), def))
 end
diff --git a/test/ITF1788_tests/libieeep1788_bool.jl b/test/ITF1788_tests/libieeep1788_bool.jl
new file mode 100644
index 000000000..4d8e63c7a
--- /dev/null
+++ b/test/ITF1788_tests/libieeep1788_bool.jl
@@ -0,0 +1,620 @@
+#=
+ 
+ Unit tests from libieeep1788 for interval boolean operations
+ (Original author: Marco Nehmeier)
+ converted into portable ITL format by Oliver Heimlich.
+ 
+ Copyright 2013-2015 Marco Nehmeier (nehmeier@informatik.uni-wuerzburg.de)
+ Copyright 2015-2017 Oliver Heimlich (oheim@posteo.de)
+ 
+ Licensed under the Apache License, Version 2.0 (the "License");
+ you may not use this file except in compliance with the License.
+ You may obtain a copy of the License at
+ 
+     http://www.apache.org/licenses/LICENSE-2.0
+ 
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License i        s distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
+ 
+=#
+#Language imports
+
+#Test library imports
+using Test
+
+#Arithmetic library imports
+using IntervalArithmetic
+
+#Preamble
+setprecision(53)
+setprecision(Interval, Float64)
+setrounding(Interval, :tight)
+# Set full format, and show decorations
+@format full
+
+@testset "minimal_is_empty_test" begin
+    @test isempty(∅)
+    @test isempty(Interval(-Inf, Inf)) == false
+    @test isempty(Interval(1.0, 2.0)) == false
+    @test isempty(Interval(-1.0, 2.0)) == false
+    @test isempty(Interval(-3.0, -2.0)) == false
+    @test isempty(Interval(-Inf, 2.0)) == false
+    @test isempty(Interval(-Inf, 0.0)) == false
+    @test isempty(Interval(-Inf, -0.0)) == false
+    @test isempty(Interval(0.0, Inf)) == false
+    @test isempty(Interval(-0.0, Inf)) == false
+    @test isempty(Interval(-0.0, 0.0)) == false
+    @test isempty(Interval(0.0, -0.0)) == false
+    @test isempty(Interval(0.0, 0.0)) == false
+    @test isempty(Interval(-0.0, -0.0)) == false
+end
+
+@testset "minimal_is_empty_dec_test" begin
+    @test isempty(nai()) == false
+    @test isempty(DecoratedInterval(∅, trv))
+    @test isempty(DecoratedInterval(Interval(-Inf, Inf), def)) == false
+    @test isempty(DecoratedInterval(Interval(1.0, 2.0), com)) == false
+    @test isempty(DecoratedInterval(Interval(-1.0, 2.0), trv)) == false
+    @test isempty(DecoratedInterval(Interval(-3.0, -2.0), dac)) == false
+    @test isempty(DecoratedInterval(Interval(-Inf, 2.0), trv)) == false
+    @test isempty(DecoratedInterval(Interval(-Inf, 0.0), trv)) == false
+    @test isempty(DecoratedInterval(Interval(-Inf, -0.0), trv)) == false
+    @test isempty(DecoratedInterval(Interval(0.0, Inf), def)) == false
+    @test isempty(DecoratedInterval(Interval(-0.0, Inf), trv)) == false
+    @test isempty(DecoratedInterval(Interval(-0.0, 0.0), com)) == false
+    @test isempty(DecoratedInterval(Interval(0.0, -0.0), trv)) == false
+    @test isempty(DecoratedInterval(Interval(0.0, 0.0), trv)) == false
+    @test isempty(DecoratedInterval(Interval(-0.0, -0.0), trv)) == false
+end
+
+@testset "minimal_is_entire_test" begin
+    @test isentire(∅) == false
+    @test isentire(Interval(-Inf, Inf))
+    @test isentire(Interval(1.0, 2.0)) == false
+    @test isentire(Interval(-1.0, 2.0)) == false
+    @test isentire(Interval(-3.0, -2.0)) == false
+    @test isentire(Interval(-Inf, 2.0)) == false
+    @test isentire(Interval(-Inf, 0.0)) == false
+    @test isentire(Interval(-Inf, -0.0)) == false
+    @test isentire(Interval(0.0, Inf)) == false
+    @test isentire(Interval(-0.0, Inf)) == false
+    @test isentire(Interval(-0.0, 0.0)) == false
+    @test isentire(Interval(0.0, -0.0)) == false
+    @test isentire(Interval(0.0, 0.0)) == false
+    @test isentire(Interval(-0.0, -0.0)) == false
+end
+
+@testset "minimal_is_entire_dec_test" begin
+    @test isentire(nai()) == false
+    @test isentire(DecoratedInterval(∅, trv)) == false
+    @test isentire(DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test isentire(DecoratedInterval(Interval(-Inf, Inf), def))
+    @test isentire(DecoratedInterval(Interval(-Inf, Inf), dac))
+    @test isentire(DecoratedInterval(Interval(1.0, 2.0), com)) == false
+    @test isentire(DecoratedInterval(Interval(-1.0, 2.0), trv)) == false
+    @test isentire(DecoratedInterval(Interval(-3.0, -2.0), dac)) == false
+    @test isentire(DecoratedInterval(Interval(-Inf, 2.0), trv)) == false
+    @test isentire(DecoratedInterval(Interval(-Inf, 0.0), trv)) == false
+    @test isentire(DecoratedInterval(Interval(-Inf, -0.0), trv)) == false
+    @test isentire(DecoratedInterval(Interval(0.0, Inf), def)) == false
+    @test isentire(DecoratedInterval(Interval(-0.0, Inf), trv)) == false
+    @test isentire(DecoratedInterval(Interval(-0.0, 0.0), com)) == false
+    @test isentire(DecoratedInterval(Interval(0.0, -0.0), trv)) == false
+    @test isentire(DecoratedInterval(Interval(0.0, 0.0), trv)) == false
+    @test isentire(DecoratedInterval(Interval(-0.0, -0.0), trv)) == false
+end
+
+@testset "minimal_is_nai_dec_test" begin
+    @test isnai(nai())
+    @test isnai(DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test isnai(DecoratedInterval(Interval(-Inf, Inf), def)) == false
+    @test isnai(DecoratedInterval(Interval(-Inf, Inf), dac)) == false
+    @test isnai(DecoratedInterval(Interval(1.0, 2.0), com)) == false
+    @test isnai(DecoratedInterval(Interval(-1.0, 2.0), trv)) == false
+    @test isnai(DecoratedInterval(Interval(-3.0, -2.0), dac)) == false
+    @test isnai(DecoratedInterval(Interval(-Inf, 2.0), trv)) == false
+    @test isnai(DecoratedInterval(Interval(-Inf, 0.0), trv)) == false
+    @test isnai(DecoratedInterval(Interval(-Inf, -0.0), trv)) == false
+    @test isnai(DecoratedInterval(Interval(0.0, Inf), def)) == false
+    @test isnai(DecoratedInterval(Interval(-0.0, Inf), trv)) == false
+    @test isnai(DecoratedInterval(Interval(-0.0, 0.0), com)) == false
+    @test isnai(DecoratedInterval(Interval(0.0, -0.0), trv)) == false
+    @test isnai(DecoratedInterval(Interval(0.0, 0.0), trv)) == false
+    @test isnai(DecoratedInterval(Interval(-0.0, -0.0), trv)) == false
+end
+
+@testset "minimal_equal_test" begin
+    @test ==(Interval(1.0, 2.0), Interval(1.0, 2.0))
+    @test ==(Interval(1.0, 2.1), Interval(1.0, 2.0)) == false
+    @test ==(∅, ∅)
+    @test ==(∅, Interval(1.0, 2.0)) == false
+    @test ==(Interval(-Inf, Inf), Interval(-Inf, Inf))
+    @test ==(Interval(1.0, 2.4), Interval(-Inf, Inf)) == false
+    @test ==(Interval(1.0, Inf), Interval(1.0, Inf))
+    @test ==(Interval(1.0, 2.4), Interval(1.0, Inf)) == false
+    @test ==(Interval(-Inf, 2.0), Interval(-Inf, 2.0))
+    @test ==(Interval(-Inf, 2.4), Interval(-Inf, 2.0)) == false
+    @test ==(Interval(-2.0, 0.0), Interval(-2.0, 0.0))
+    @test ==(Interval(-0.0, 2.0), Interval(0.0, 2.0))
+    @test ==(Interval(-0.0, -0.0), Interval(0.0, 0.0))
+    @test ==(Interval(-0.0, 0.0), Interval(0.0, 0.0))
+    @test ==(Interval(0.0, -0.0), Interval(0.0, 0.0))
+end
+
+@testset "minimal_equal_dec_test" begin
+    @test ==(DecoratedInterval(Interval(1.0, 2.0), def), DecoratedInterval(Interval(1.0, 2.0), trv))
+    @test ==(DecoratedInterval(Interval(1.0, 2.1), trv), DecoratedInterval(Interval(1.0, 2.0), trv)) == false
+    @test ==(DecoratedInterval(∅, trv), DecoratedInterval(∅, trv))
+    @test ==(DecoratedInterval(∅, trv), nai()) == false
+    @test ==(nai(), DecoratedInterval(∅, trv)) == false
+    @test ==(nai(), nai()) == false
+    @test ==(DecoratedInterval(∅, trv), DecoratedInterval(Interval(1.0, 2.0), trv)) == false
+    @test ==(nai(), DecoratedInterval(Interval(1.0, 2.0), trv)) == false
+    @test ==(DecoratedInterval(Interval(-Inf, Inf), def), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test ==(DecoratedInterval(Interval(1.0, 2.4), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test ==(DecoratedInterval(Interval(1.0, Inf), trv), DecoratedInterval(Interval(1.0, Inf), trv))
+    @test ==(DecoratedInterval(Interval(1.0, 2.4), def), DecoratedInterval(Interval(1.0, Inf), trv)) == false
+    @test ==(DecoratedInterval(Interval(-Inf, 2.0), trv), DecoratedInterval(Interval(-Inf, 2.0), trv))
+    @test ==(DecoratedInterval(Interval(-Inf, 2.4), def), DecoratedInterval(Interval(-Inf, 2.0), trv)) == false
+    @test ==(DecoratedInterval(Interval(-2.0, 0.0), trv), DecoratedInterval(Interval(-2.0, 0.0), trv))
+    @test ==(DecoratedInterval(Interval(-0.0, 2.0), def), DecoratedInterval(Interval(0.0, 2.0), trv))
+    @test ==(DecoratedInterval(Interval(-0.0, -0.0), trv), DecoratedInterval(Interval(0.0, 0.0), trv))
+    @test ==(DecoratedInterval(Interval(-0.0, 0.0), def), DecoratedInterval(Interval(0.0, 0.0), trv))
+    @test ==(DecoratedInterval(Interval(0.0, -0.0), trv), DecoratedInterval(Interval(0.0, 0.0), trv))
+end
+
+@testset "minimal_subset_test" begin
+    @test ⊆(∅, ∅)
+    @test ⊆(∅, Interval(0.0, 4.0))
+    @test ⊆(∅, Interval(-0.0, 4.0))
+    @test ⊆(∅, Interval(-0.1, 1.0))
+    @test ⊆(∅, Interval(-0.1, 0.0))
+    @test ⊆(∅, Interval(-0.1, -0.0))
+    @test ⊆(∅, Interval(-Inf, Inf))
+    @test ⊆(Interval(0.0, 4.0), ∅) == false
+    @test ⊆(Interval(-0.0, 4.0), ∅) == false
+    @test ⊆(Interval(-0.1, 1.0), ∅) == false
+    @test ⊆(Interval(-Inf, Inf), ∅) == false
+    @test ⊆(Interval(0.0, 4.0), Interval(-Inf, Inf))
+    @test ⊆(Interval(-0.0, 4.0), Interval(-Inf, Inf))
+    @test ⊆(Interval(-0.1, 1.0), Interval(-Inf, Inf))
+    @test ⊆(Interval(-Inf, Inf), Interval(-Inf, Inf))
+    @test ⊆(Interval(1.0, 2.0), Interval(1.0, 2.0))
+    @test ⊆(Interval(1.0, 2.0), Interval(0.0, 4.0))
+    @test ⊆(Interval(1.0, 2.0), Interval(-0.0, 4.0))
+    @test ⊆(Interval(0.1, 0.2), Interval(0.0, 4.0))
+    @test ⊆(Interval(0.1, 0.2), Interval(-0.0, 4.0))
+    @test ⊆(Interval(-0.1, -0.1), Interval(-4.0, 3.4))
+    @test ⊆(Interval(0.0, 0.0), Interval(-0.0, -0.0))
+    @test ⊆(Interval(-0.0, -0.0), Interval(0.0, 0.0))
+    @test ⊆(Interval(-0.0, 0.0), Interval(0.0, 0.0))
+    @test ⊆(Interval(-0.0, 0.0), Interval(0.0, -0.0))
+    @test ⊆(Interval(0.0, -0.0), Interval(0.0, 0.0))
+    @test ⊆(Interval(0.0, -0.0), Interval(-0.0, 0.0))
+end
+
+@testset "minimal_subset_dec_test" begin
+    @test ⊆(nai(), nai()) == false
+    @test ⊆(nai(), DecoratedInterval(∅, trv)) == false
+    @test ⊆(nai(), DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test ⊆(DecoratedInterval(∅, trv), DecoratedInterval(Interval(0.0, 4.0), trv))
+    @test ⊆(DecoratedInterval(∅, trv), DecoratedInterval(Interval(-0.0, 4.0), def))
+    @test ⊆(DecoratedInterval(∅, trv), DecoratedInterval(Interval(-0.1, 1.0), trv))
+    @test ⊆(DecoratedInterval(∅, trv), DecoratedInterval(Interval(-0.1, 0.0), trv))
+    @test ⊆(DecoratedInterval(∅, trv), DecoratedInterval(Interval(-0.1, -0.0), trv))
+    @test ⊆(DecoratedInterval(∅, trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test ⊆(DecoratedInterval(Interval(0.0, 4.0), trv), DecoratedInterval(∅, trv)) == false
+    @test ⊆(DecoratedInterval(Interval(-0.0, 4.0), def), DecoratedInterval(∅, trv)) == false
+    @test ⊆(DecoratedInterval(Interval(-0.1, 1.0), trv), DecoratedInterval(∅, trv)) == false
+    @test ⊆(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(∅, trv)) == false
+    @test ⊆(DecoratedInterval(Interval(0.0, 4.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test ⊆(DecoratedInterval(Interval(-0.0, 4.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test ⊆(DecoratedInterval(Interval(-0.1, 1.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test ⊆(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test ⊆(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(Interval(1.0, 2.0), trv))
+    @test ⊆(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(Interval(0.0, 4.0), trv))
+    @test ⊆(DecoratedInterval(Interval(1.0, 2.0), def), DecoratedInterval(Interval(-0.0, 4.0), def))
+    @test ⊆(DecoratedInterval(Interval(0.1, 0.2), trv), DecoratedInterval(Interval(0.0, 4.0), trv))
+    @test ⊆(DecoratedInterval(Interval(0.1, 0.2), trv), DecoratedInterval(Interval(-0.0, 4.0), def))
+    @test ⊆(DecoratedInterval(Interval(-0.1, -0.1), trv), DecoratedInterval(Interval(-4.0, 3.4), trv))
+    @test ⊆(DecoratedInterval(Interval(0.0, 0.0), trv), DecoratedInterval(Interval(-0.0, -0.0), trv))
+    @test ⊆(DecoratedInterval(Interval(-0.0, -0.0), trv), DecoratedInterval(Interval(0.0, 0.0), def))
+    @test ⊆(DecoratedInterval(Interval(-0.0, 0.0), trv), DecoratedInterval(Interval(0.0, 0.0), trv))
+    @test ⊆(DecoratedInterval(Interval(-0.0, 0.0), trv), DecoratedInterval(Interval(0.0, -0.0), trv))
+    @test ⊆(DecoratedInterval(Interval(0.0, -0.0), def), DecoratedInterval(Interval(0.0, 0.0), trv))
+    @test ⊆(DecoratedInterval(Interval(0.0, -0.0), trv), DecoratedInterval(Interval(-0.0, 0.0), trv))
+end
+
+@testset "minimal_less_test" begin
+    @test ≤(∅, ∅)
+    @test (∅ ≤ ∅)
+    @test ≤(Interval(1.0, 2.0), ∅) == false
+    @test (Interval(1.0, 2.0) ≤ ∅) == false
+    @test ≤(∅, Interval(1.0, 2.0)) == false
+    @test (∅ ≤ Interval(1.0, 2.0)) == false
+    @test ≤(Interval(-Inf, Inf), Interval(-Inf, Inf))
+    @test (Interval(-Inf, Inf) ≤ Interval(-Inf, Inf))
+    @test ≤(Interval(1.0, 2.0), Interval(-Inf, Inf)) == false
+    @test (Interval(1.0, 2.0) ≤ Interval(-Inf, Inf)) == false
+    @test ≤(Interval(0.0, 2.0), Interval(-Inf, Inf)) == false
+    @test (Interval(0.0, 2.0) ≤ Interval(-Inf, Inf)) == false
+    @test ≤(Interval(-0.0, 2.0), Interval(-Inf, Inf)) == false
+    @test (Interval(-0.0, 2.0) ≤ Interval(-Inf, Inf)) == false
+    @test ≤(Interval(-Inf, Inf), Interval(1.0, 2.0)) == false
+    @test (Interval(-Inf, Inf) ≤ Interval(1.0, 2.0)) == false
+    @test ≤(Interval(-Inf, Inf), Interval(0.0, 2.0)) == false
+    @test (Interval(-Inf, Inf) ≤ Interval(0.0, 2.0)) == false
+    @test ≤(Interval(-Inf, Inf), Interval(-0.0, 2.0)) == false
+    @test (Interval(-Inf, Inf) ≤ Interval(-0.0, 2.0)) == false
+    @test ≤(Interval(0.0, 2.0), Interval(0.0, 2.0))
+    @test (Interval(0.0, 2.0) ≤ Interval(0.0, 2.0))
+    @test ≤(Interval(0.0, 2.0), Interval(-0.0, 2.0))
+    @test (Interval(0.0, 2.0) ≤ Interval(-0.0, 2.0))
+    @test ≤(Interval(0.0, 2.0), Interval(1.0, 2.0))
+    @test (Interval(0.0, 2.0) ≤ Interval(1.0, 2.0))
+    @test ≤(Interval(-0.0, 2.0), Interval(1.0, 2.0))
+    @test (Interval(-0.0, 2.0) ≤ Interval(1.0, 2.0))
+    @test ≤(Interval(1.0, 2.0), Interval(1.0, 2.0))
+    @test (Interval(1.0, 2.0) ≤ Interval(1.0, 2.0))
+    @test ≤(Interval(1.0, 2.0), Interval(3.0, 4.0))
+    @test (Interval(1.0, 2.0) ≤ Interval(3.0, 4.0))
+    @test ≤(Interval(1.0, 3.5), Interval(3.0, 4.0))
+    @test (Interval(1.0, 3.5) ≤ Interval(3.0, 4.0))
+    @test ≤(Interval(1.0, 4.0), Interval(3.0, 4.0))
+    @test (Interval(1.0, 4.0) ≤ Interval(3.0, 4.0))
+    @test ≤(Interval(-2.0, -1.0), Interval(-2.0, -1.0))
+    @test (Interval(-2.0, -1.0) ≤ Interval(-2.0, -1.0))
+    @test ≤(Interval(-3.0, -1.5), Interval(-2.0, -1.0))
+    @test (Interval(-3.0, -1.5) ≤ Interval(-2.0, -1.0))
+    @test ≤(Interval(0.0, 0.0), Interval(-0.0, -0.0))
+    @test (Interval(0.0, 0.0) ≤ Interval(-0.0, -0.0))
+    @test ≤(Interval(-0.0, -0.0), Interval(0.0, 0.0))
+    @test (Interval(-0.0, -0.0) ≤ Interval(0.0, 0.0))
+    @test ≤(Interval(-0.0, 0.0), Interval(0.0, 0.0))
+    @test (Interval(-0.0, 0.0) ≤ Interval(0.0, 0.0))
+    @test ≤(Interval(-0.0, 0.0), Interval(0.0, -0.0))
+    @test (Interval(-0.0, 0.0) ≤ Interval(0.0, -0.0))
+    @test ≤(Interval(0.0, -0.0), Interval(0.0, 0.0))
+    @test (Interval(0.0, -0.0) ≤ Interval(0.0, 0.0))
+    @test ≤(Interval(0.0, -0.0), Interval(-0.0, 0.0))
+    @test (Interval(0.0, -0.0) ≤ Interval(-0.0, 0.0))
+end
+
+@testset "minimal_less_dec_test" begin
+    @test ≤(nai(), nai()) == false
+    @test (nai() ≤ nai()) == false
+    @test ≤(DecoratedInterval(∅, trv), nai()) == false
+    @test (DecoratedInterval(∅, trv) ≤ nai()) == false
+    @test ≤(DecoratedInterval(Interval(1.0, 2.0), trv), nai()) == false
+    @test (DecoratedInterval(Interval(1.0, 2.0), trv) ≤ nai()) == false
+    @test ≤(nai(), DecoratedInterval(Interval(1.0, 2.0), def)) == false
+    @test (nai() ≤ DecoratedInterval(Interval(1.0, 2.0), def)) == false
+    @test ≤(DecoratedInterval(∅, trv), DecoratedInterval(∅, trv))
+    @test (DecoratedInterval(∅, trv) ≤ DecoratedInterval(∅, trv))
+    @test ≤(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(∅, trv)) == false
+    @test (DecoratedInterval(Interval(1.0, 2.0), trv) ≤ DecoratedInterval(∅, trv)) == false
+    @test ≤(DecoratedInterval(∅, trv), DecoratedInterval(Interval(1.0, 2.0), trv)) == false
+    @test (DecoratedInterval(∅, trv) ≤ DecoratedInterval(Interval(1.0, 2.0), trv)) == false
+    @test ≤(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test (DecoratedInterval(Interval(-Inf, Inf), trv) ≤ DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test ≤(DecoratedInterval(Interval(1.0, 2.0), def), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test (DecoratedInterval(Interval(1.0, 2.0), def) ≤ DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test ≤(DecoratedInterval(Interval(0.0, 2.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test (DecoratedInterval(Interval(0.0, 2.0), trv) ≤ DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test ≤(DecoratedInterval(Interval(-0.0, 2.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test (DecoratedInterval(Interval(-0.0, 2.0), trv) ≤ DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test ≤(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(1.0, 2.0), trv)) == false
+    @test (DecoratedInterval(Interval(-Inf, Inf), trv) ≤ DecoratedInterval(Interval(1.0, 2.0), trv)) == false
+    @test ≤(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(0.0, 2.0), def)) == false
+    @test (DecoratedInterval(Interval(-Inf, Inf), trv) ≤ DecoratedInterval(Interval(0.0, 2.0), def)) == false
+    @test ≤(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(-0.0, 2.0), trv)) == false
+    @test (DecoratedInterval(Interval(-Inf, Inf), trv) ≤ DecoratedInterval(Interval(-0.0, 2.0), trv)) == false
+    @test ≤(DecoratedInterval(Interval(0.0, 2.0), trv), DecoratedInterval(Interval(0.0, 2.0), trv))
+    @test (DecoratedInterval(Interval(0.0, 2.0), trv) ≤ DecoratedInterval(Interval(0.0, 2.0), trv))
+    @test ≤(DecoratedInterval(Interval(0.0, 2.0), trv), DecoratedInterval(Interval(-0.0, 2.0), trv))
+    @test (DecoratedInterval(Interval(0.0, 2.0), trv) ≤ DecoratedInterval(Interval(-0.0, 2.0), trv))
+    @test ≤(DecoratedInterval(Interval(0.0, 2.0), def), DecoratedInterval(Interval(1.0, 2.0), def))
+    @test (DecoratedInterval(Interval(0.0, 2.0), def) ≤ DecoratedInterval(Interval(1.0, 2.0), def))
+    @test ≤(DecoratedInterval(Interval(-0.0, 2.0), trv), DecoratedInterval(Interval(1.0, 2.0), trv))
+    @test (DecoratedInterval(Interval(-0.0, 2.0), trv) ≤ DecoratedInterval(Interval(1.0, 2.0), trv))
+    @test ≤(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(Interval(1.0, 2.0), trv))
+    @test (DecoratedInterval(Interval(1.0, 2.0), trv) ≤ DecoratedInterval(Interval(1.0, 2.0), trv))
+    @test ≤(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(Interval(3.0, 4.0), def))
+    @test (DecoratedInterval(Interval(1.0, 2.0), trv) ≤ DecoratedInterval(Interval(3.0, 4.0), def))
+    @test ≤(DecoratedInterval(Interval(1.0, 3.5), trv), DecoratedInterval(Interval(3.0, 4.0), trv))
+    @test (DecoratedInterval(Interval(1.0, 3.5), trv) ≤ DecoratedInterval(Interval(3.0, 4.0), trv))
+    @test ≤(DecoratedInterval(Interval(1.0, 4.0), trv), DecoratedInterval(Interval(3.0, 4.0), trv))
+    @test (DecoratedInterval(Interval(1.0, 4.0), trv) ≤ DecoratedInterval(Interval(3.0, 4.0), trv))
+    @test ≤(DecoratedInterval(Interval(-2.0, -1.0), trv), DecoratedInterval(Interval(-2.0, -1.0), trv))
+    @test (DecoratedInterval(Interval(-2.0, -1.0), trv) ≤ DecoratedInterval(Interval(-2.0, -1.0), trv))
+    @test ≤(DecoratedInterval(Interval(-3.0, -1.5), trv), DecoratedInterval(Interval(-2.0, -1.0), trv))
+    @test (DecoratedInterval(Interval(-3.0, -1.5), trv) ≤ DecoratedInterval(Interval(-2.0, -1.0), trv))
+    @test ≤(DecoratedInterval(Interval(0.0, 0.0), trv), DecoratedInterval(Interval(-0.0, -0.0), trv))
+    @test (DecoratedInterval(Interval(0.0, 0.0), trv) ≤ DecoratedInterval(Interval(-0.0, -0.0), trv))
+    @test ≤(DecoratedInterval(Interval(-0.0, -0.0), trv), DecoratedInterval(Interval(0.0, 0.0), def))
+    @test (DecoratedInterval(Interval(-0.0, -0.0), trv) ≤ DecoratedInterval(Interval(0.0, 0.0), def))
+    @test ≤(DecoratedInterval(Interval(-0.0, 0.0), trv), DecoratedInterval(Interval(0.0, 0.0), trv))
+    @test (DecoratedInterval(Interval(-0.0, 0.0), trv) ≤ DecoratedInterval(Interval(0.0, 0.0), trv))
+    @test ≤(DecoratedInterval(Interval(-0.0, 0.0), trv), DecoratedInterval(Interval(0.0, -0.0), trv))
+    @test (DecoratedInterval(Interval(-0.0, 0.0), trv) ≤ DecoratedInterval(Interval(0.0, -0.0), trv))
+    @test ≤(DecoratedInterval(Interval(0.0, -0.0), def), DecoratedInterval(Interval(0.0, 0.0), trv))
+    @test (DecoratedInterval(Interval(0.0, -0.0), def) ≤ DecoratedInterval(Interval(0.0, 0.0), trv))
+    @test ≤(DecoratedInterval(Interval(0.0, -0.0), trv), DecoratedInterval(Interval(-0.0, 0.0), trv))
+    @test (DecoratedInterval(Interval(0.0, -0.0), trv) ≤ DecoratedInterval(Interval(-0.0, 0.0), trv))
+end
+
+@testset "minimal_precedes_test" begin
+    @test precedes(∅, Interval(3.0, 4.0))
+    @test precedes(Interval(3.0, 4.0), ∅)
+    @test precedes(∅, ∅)
+    @test precedes(Interval(1.0, 2.0), Interval(-Inf, Inf)) == false
+    @test precedes(Interval(0.0, 2.0), Interval(-Inf, Inf)) == false
+    @test precedes(Interval(-0.0, 2.0), Interval(-Inf, Inf)) == false
+    @test precedes(Interval(-Inf, Inf), Interval(1.0, 2.0)) == false
+    @test precedes(Interval(-Inf, Inf), Interval(-Inf, Inf)) == false
+    @test precedes(Interval(1.0, 2.0), Interval(3.0, 4.0))
+    @test precedes(Interval(1.0, 3.0), Interval(3.0, 4.0))
+    @test precedes(Interval(-3.0, -1.0), Interval(-1.0, 0.0))
+    @test precedes(Interval(-3.0, -1.0), Interval(-1.0, -0.0))
+    @test precedes(Interval(1.0, 3.5), Interval(3.0, 4.0)) == false
+    @test precedes(Interval(1.0, 4.0), Interval(3.0, 4.0)) == false
+    @test precedes(Interval(-3.0, -0.1), Interval(-1.0, 0.0)) == false
+    @test precedes(Interval(0.0, 0.0), Interval(-0.0, -0.0))
+    @test precedes(Interval(-0.0, -0.0), Interval(0.0, 0.0))
+    @test precedes(Interval(-0.0, 0.0), Interval(0.0, 0.0))
+    @test precedes(Interval(-0.0, 0.0), Interval(0.0, -0.0))
+    @test precedes(Interval(0.0, -0.0), Interval(0.0, 0.0))
+    @test precedes(Interval(0.0, -0.0), Interval(-0.0, 0.0))
+end
+
+@testset "minimal_precedes_dec_test" begin
+    @test precedes(nai(), DecoratedInterval(Interval(3.0, 4.0), def)) == false
+    @test precedes(DecoratedInterval(Interval(3.0, 4.0), trv), nai()) == false
+    @test precedes(nai(), DecoratedInterval(∅, trv)) == false
+    @test precedes(nai(), nai()) == false
+    @test precedes(DecoratedInterval(∅, trv), DecoratedInterval(Interval(3.0, 4.0), def))
+    @test precedes(DecoratedInterval(Interval(3.0, 4.0), trv), DecoratedInterval(∅, trv))
+    @test precedes(DecoratedInterval(∅, trv), DecoratedInterval(∅, trv))
+    @test precedes(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test precedes(DecoratedInterval(Interval(0.0, 2.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test precedes(DecoratedInterval(Interval(-0.0, 2.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test precedes(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(1.0, 2.0), trv)) == false
+    @test precedes(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test precedes(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(Interval(3.0, 4.0), trv))
+    @test precedes(DecoratedInterval(Interval(1.0, 3.0), trv), DecoratedInterval(Interval(3.0, 4.0), def))
+    @test precedes(DecoratedInterval(Interval(-3.0, -1.0), def), DecoratedInterval(Interval(-1.0, 0.0), trv))
+    @test precedes(DecoratedInterval(Interval(-3.0, -1.0), trv), DecoratedInterval(Interval(-1.0, -0.0), trv))
+    @test precedes(DecoratedInterval(Interval(1.0, 3.5), trv), DecoratedInterval(Interval(3.0, 4.0), trv)) == false
+    @test precedes(DecoratedInterval(Interval(1.0, 4.0), trv), DecoratedInterval(Interval(3.0, 4.0), trv)) == false
+    @test precedes(DecoratedInterval(Interval(-3.0, -0.1), trv), DecoratedInterval(Interval(-1.0, 0.0), trv)) == false
+    @test precedes(DecoratedInterval(Interval(0.0, 0.0), trv), DecoratedInterval(Interval(-0.0, -0.0), trv))
+    @test precedes(DecoratedInterval(Interval(-0.0, -0.0), trv), DecoratedInterval(Interval(0.0, 0.0), def))
+    @test precedes(DecoratedInterval(Interval(-0.0, 0.0), trv), DecoratedInterval(Interval(0.0, 0.0), trv))
+    @test precedes(DecoratedInterval(Interval(-0.0, 0.0), def), DecoratedInterval(Interval(0.0, -0.0), trv))
+    @test precedes(DecoratedInterval(Interval(0.0, -0.0), trv), DecoratedInterval(Interval(0.0, 0.0), trv))
+    @test precedes(DecoratedInterval(Interval(0.0, -0.0), trv), DecoratedInterval(Interval(-0.0, 0.0), trv))
+end
+
+@testset "minimal_interior_test" begin
+    @test ⪽(∅, ∅)
+    @test isinterior(∅, ∅)
+    @test (∅ ⪽ ∅)
+    @test ⪽(∅, Interval(0.0, 4.0))
+    @test isinterior(∅, Interval(0.0, 4.0))
+    @test (∅ ⪽ Interval(0.0, 4.0))
+    @test ⪽(Interval(0.0, 4.0), ∅) == false
+    @test isinterior(Interval(0.0, 4.0), ∅) == false
+    @test (Interval(0.0, 4.0) ⪽ ∅) == false
+    @test ⪽(Interval(-Inf, Inf), Interval(-Inf, Inf))
+    @test isinterior(Interval(-Inf, Inf), Interval(-Inf, Inf))
+    @test (Interval(-Inf, Inf) ⪽ Interval(-Inf, Inf))
+    @test ⪽(Interval(0.0, 4.0), Interval(-Inf, Inf))
+    @test isinterior(Interval(0.0, 4.0), Interval(-Inf, Inf))
+    @test (Interval(0.0, 4.0) ⪽ Interval(-Inf, Inf))
+    @test ⪽(∅, Interval(-Inf, Inf))
+    @test isinterior(∅, Interval(-Inf, Inf))
+    @test (∅ ⪽ Interval(-Inf, Inf))
+    @test ⪽(Interval(-Inf, Inf), Interval(0.0, 4.0)) == false
+    @test isinterior(Interval(-Inf, Inf), Interval(0.0, 4.0)) == false
+    @test (Interval(-Inf, Inf) ⪽ Interval(0.0, 4.0)) == false
+    @test ⪽(Interval(0.0, 4.0), Interval(0.0, 4.0)) == false
+    @test isinterior(Interval(0.0, 4.0), Interval(0.0, 4.0)) == false
+    @test (Interval(0.0, 4.0) ⪽ Interval(0.0, 4.0)) == false
+    @test ⪽(Interval(1.0, 2.0), Interval(0.0, 4.0))
+    @test isinterior(Interval(1.0, 2.0), Interval(0.0, 4.0))
+    @test (Interval(1.0, 2.0) ⪽ Interval(0.0, 4.0))
+    @test ⪽(Interval(-2.0, 2.0), Interval(-2.0, 4.0)) == false
+    @test isinterior(Interval(-2.0, 2.0), Interval(-2.0, 4.0)) == false
+    @test (Interval(-2.0, 2.0) ⪽ Interval(-2.0, 4.0)) == false
+    @test ⪽(Interval(-0.0, -0.0), Interval(-2.0, 4.0))
+    @test isinterior(Interval(-0.0, -0.0), Interval(-2.0, 4.0))
+    @test (Interval(-0.0, -0.0) ⪽ Interval(-2.0, 4.0))
+    @test ⪽(Interval(0.0, 0.0), Interval(-2.0, 4.0))
+    @test isinterior(Interval(0.0, 0.0), Interval(-2.0, 4.0))
+    @test (Interval(0.0, 0.0) ⪽ Interval(-2.0, 4.0))
+    @test ⪽(Interval(0.0, 0.0), Interval(-0.0, -0.0)) == false
+    @test isinterior(Interval(0.0, 0.0), Interval(-0.0, -0.0)) == false
+    @test (Interval(0.0, 0.0) ⪽ Interval(-0.0, -0.0)) == false
+    @test ⪽(Interval(0.0, 4.4), Interval(0.0, 4.0)) == false
+    @test isinterior(Interval(0.0, 4.4), Interval(0.0, 4.0)) == false
+    @test (Interval(0.0, 4.4) ⪽ Interval(0.0, 4.0)) == false
+    @test ⪽(Interval(-1.0, -1.0), Interval(0.0, 4.0)) == false
+    @test isinterior(Interval(-1.0, -1.0), Interval(0.0, 4.0)) == false
+    @test (Interval(-1.0, -1.0) ⪽ Interval(0.0, 4.0)) == false
+    @test ⪽(Interval(2.0, 2.0), Interval(-2.0, -1.0)) == false
+    @test isinterior(Interval(2.0, 2.0), Interval(-2.0, -1.0)) == false
+    @test (Interval(2.0, 2.0) ⪽ Interval(-2.0, -1.0)) == false
+end
+
+@testset "minimal_interior_dec_test" begin
+    @test ⪽(nai(), nai()) == false
+    @test isinterior(nai(), nai()) == false
+    @test (nai() ⪽ nai()) == false
+    @test ⪽(nai(), DecoratedInterval(∅, trv)) == false
+    @test isinterior(nai(), DecoratedInterval(∅, trv)) == false
+    @test (nai() ⪽ DecoratedInterval(∅, trv)) == false
+    @test ⪽(nai(), DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test isinterior(nai(), DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test (nai() ⪽ DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test ⪽(DecoratedInterval(Interval(0.0, 4.0), def), nai()) == false
+    @test isinterior(DecoratedInterval(Interval(0.0, 4.0), def), nai()) == false
+    @test (DecoratedInterval(Interval(0.0, 4.0), def) ⪽ nai()) == false
+    @test ⪽(DecoratedInterval(∅, trv), DecoratedInterval(∅, trv))
+    @test isinterior(DecoratedInterval(∅, trv), DecoratedInterval(∅, trv))
+    @test (DecoratedInterval(∅, trv) ⪽ DecoratedInterval(∅, trv))
+    @test ⪽(DecoratedInterval(∅, trv), DecoratedInterval(Interval(0.0, 4.0), trv))
+    @test isinterior(DecoratedInterval(∅, trv), DecoratedInterval(Interval(0.0, 4.0), trv))
+    @test (DecoratedInterval(∅, trv) ⪽ DecoratedInterval(Interval(0.0, 4.0), trv))
+    @test ⪽(DecoratedInterval(Interval(0.0, 4.0), def), DecoratedInterval(∅, trv)) == false
+    @test isinterior(DecoratedInterval(Interval(0.0, 4.0), def), DecoratedInterval(∅, trv)) == false
+    @test (DecoratedInterval(Interval(0.0, 4.0), def) ⪽ DecoratedInterval(∅, trv)) == false
+    @test ⪽(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test isinterior(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test (DecoratedInterval(Interval(-Inf, Inf), trv) ⪽ DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test ⪽(DecoratedInterval(Interval(0.0, 4.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test isinterior(DecoratedInterval(Interval(0.0, 4.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test (DecoratedInterval(Interval(0.0, 4.0), trv) ⪽ DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test ⪽(DecoratedInterval(∅, trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test isinterior(DecoratedInterval(∅, trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test (DecoratedInterval(∅, trv) ⪽ DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test ⪽(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test isinterior(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test (DecoratedInterval(Interval(-Inf, Inf), trv) ⪽ DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test ⪽(DecoratedInterval(Interval(0.0, 4.0), trv), DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test isinterior(DecoratedInterval(Interval(0.0, 4.0), trv), DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test (DecoratedInterval(Interval(0.0, 4.0), trv) ⪽ DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test ⪽(DecoratedInterval(Interval(1.0, 2.0), def), DecoratedInterval(Interval(0.0, 4.0), trv))
+    @test isinterior(DecoratedInterval(Interval(1.0, 2.0), def), DecoratedInterval(Interval(0.0, 4.0), trv))
+    @test (DecoratedInterval(Interval(1.0, 2.0), def) ⪽ DecoratedInterval(Interval(0.0, 4.0), trv))
+    @test ⪽(DecoratedInterval(Interval(-2.0, 2.0), trv), DecoratedInterval(Interval(-2.0, 4.0), def)) == false
+    @test isinterior(DecoratedInterval(Interval(-2.0, 2.0), trv), DecoratedInterval(Interval(-2.0, 4.0), def)) == false
+    @test (DecoratedInterval(Interval(-2.0, 2.0), trv) ⪽ DecoratedInterval(Interval(-2.0, 4.0), def)) == false
+    @test ⪽(DecoratedInterval(Interval(-0.0, -0.0), trv), DecoratedInterval(Interval(-2.0, 4.0), trv))
+    @test isinterior(DecoratedInterval(Interval(-0.0, -0.0), trv), DecoratedInterval(Interval(-2.0, 4.0), trv))
+    @test (DecoratedInterval(Interval(-0.0, -0.0), trv) ⪽ DecoratedInterval(Interval(-2.0, 4.0), trv))
+    @test ⪽(DecoratedInterval(Interval(0.0, 0.0), def), DecoratedInterval(Interval(-2.0, 4.0), trv))
+    @test isinterior(DecoratedInterval(Interval(0.0, 0.0), def), DecoratedInterval(Interval(-2.0, 4.0), trv))
+    @test (DecoratedInterval(Interval(0.0, 0.0), def) ⪽ DecoratedInterval(Interval(-2.0, 4.0), trv))
+    @test ⪽(DecoratedInterval(Interval(0.0, 0.0), trv), DecoratedInterval(Interval(-0.0, -0.0), trv)) == false
+    @test isinterior(DecoratedInterval(Interval(0.0, 0.0), trv), DecoratedInterval(Interval(-0.0, -0.0), trv)) == false
+    @test (DecoratedInterval(Interval(0.0, 0.0), trv) ⪽ DecoratedInterval(Interval(-0.0, -0.0), trv)) == false
+    @test ⪽(DecoratedInterval(Interval(0.0, 4.4), trv), DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test isinterior(DecoratedInterval(Interval(0.0, 4.4), trv), DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test (DecoratedInterval(Interval(0.0, 4.4), trv) ⪽ DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test ⪽(DecoratedInterval(Interval(-1.0, -1.0), trv), DecoratedInterval(Interval(0.0, 4.0), def)) == false
+    @test isinterior(DecoratedInterval(Interval(-1.0, -1.0), trv), DecoratedInterval(Interval(0.0, 4.0), def)) == false
+    @test (DecoratedInterval(Interval(-1.0, -1.0), trv) ⪽ DecoratedInterval(Interval(0.0, 4.0), def)) == false
+    @test ⪽(DecoratedInterval(Interval(2.0, 2.0), def), DecoratedInterval(Interval(-2.0, -1.0), trv)) == false
+    @test isinterior(DecoratedInterval(Interval(2.0, 2.0), def), DecoratedInterval(Interval(-2.0, -1.0), trv)) == false
+    @test (DecoratedInterval(Interval(2.0, 2.0), def) ⪽ DecoratedInterval(Interval(-2.0, -1.0), trv)) == false
+end
+
+@testset "minimal_strictly_less_test" begin
+    @test <(∅, ∅)
+    @test <(Interval(1.0, 2.0), ∅) == false
+    @test <(∅, Interval(1.0, 2.0)) == false
+    @test <(Interval(-Inf, Inf), Interval(-Inf, Inf))
+    @test <(Interval(1.0, 2.0), Interval(-Inf, Inf)) == false
+    @test <(Interval(-Inf, Inf), Interval(1.0, 2.0)) == false
+    @test <(Interval(1.0, 2.0), Interval(1.0, 2.0)) == false
+    @test <(Interval(1.0, 2.0), Interval(3.0, 4.0))
+    @test <(Interval(1.0, 3.5), Interval(3.0, 4.0))
+    @test <(Interval(1.0, 4.0), Interval(3.0, 4.0)) == false
+    @test <(Interval(0.0, 4.0), Interval(0.0, 4.0)) == false
+    @test <(Interval(-0.0, 4.0), Interval(0.0, 4.0)) == false
+    @test <(Interval(-2.0, -1.0), Interval(-2.0, -1.0)) == false
+    @test <(Interval(-3.0, -1.5), Interval(-2.0, -1.0))
+end
+
+@testset "minimal_strictly_less_dec_test" begin
+    @test <(nai(), nai()) == false
+    @test <(DecoratedInterval(∅, trv), nai()) == false
+    @test <(DecoratedInterval(Interval(1.0, 2.0), trv), nai()) == false
+    @test <(nai(), DecoratedInterval(Interval(1.0, 2.0), def)) == false
+    @test <(DecoratedInterval(∅, trv), DecoratedInterval(∅, trv))
+    @test <(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(∅, trv)) == false
+    @test <(DecoratedInterval(∅, trv), DecoratedInterval(Interval(1.0, 2.0), def)) == false
+    @test <(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(-Inf, Inf), trv))
+    @test <(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test <(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(1.0, 2.0), trv)) == false
+    @test <(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(Interval(1.0, 2.0), trv)) == false
+    @test <(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(Interval(3.0, 4.0), trv))
+    @test <(DecoratedInterval(Interval(1.0, 3.5), def), DecoratedInterval(Interval(3.0, 4.0), trv))
+    @test <(DecoratedInterval(Interval(1.0, 4.0), trv), DecoratedInterval(Interval(3.0, 4.0), def)) == false
+    @test <(DecoratedInterval(Interval(0.0, 4.0), trv), DecoratedInterval(Interval(0.0, 4.0), def)) == false
+    @test <(DecoratedInterval(Interval(-0.0, 4.0), def), DecoratedInterval(Interval(0.0, 4.0), trv)) == false
+    @test <(DecoratedInterval(Interval(-2.0, -1.0), def), DecoratedInterval(Interval(-2.0, -1.0), def)) == false
+    @test <(DecoratedInterval(Interval(-3.0, -1.5), trv), DecoratedInterval(Interval(-2.0, -1.0), trv))
+end
+
+@testset "minimal_strictly_precedes_test" begin
+    @test strictprecedes(∅, Interval(3.0, 4.0))
+    @test strictprecedes(Interval(3.0, 4.0), ∅)
+    @test strictprecedes(∅, ∅)
+    @test strictprecedes(Interval(1.0, 2.0), Interval(-Inf, Inf)) == false
+    @test strictprecedes(Interval(-Inf, Inf), Interval(1.0, 2.0)) == false
+    @test strictprecedes(Interval(-Inf, Inf), Interval(-Inf, Inf)) == false
+    @test strictprecedes(Interval(1.0, 2.0), Interval(3.0, 4.0))
+    @test strictprecedes(Interval(1.0, 3.0), Interval(3.0, 4.0)) == false
+    @test strictprecedes(Interval(-3.0, -1.0), Interval(-1.0, 0.0)) == false
+    @test strictprecedes(Interval(-3.0, -0.0), Interval(0.0, 1.0)) == false
+    @test strictprecedes(Interval(-3.0, 0.0), Interval(-0.0, 1.0)) == false
+    @test strictprecedes(Interval(1.0, 3.5), Interval(3.0, 4.0)) == false
+    @test strictprecedes(Interval(1.0, 4.0), Interval(3.0, 4.0)) == false
+    @test strictprecedes(Interval(-3.0, -0.1), Interval(-1.0, 0.0)) == false
+end
+
+@testset "minimal_strictly_precedes_dec_test" begin
+    @test strictprecedes(nai(), DecoratedInterval(Interval(3.0, 4.0), trv)) == false
+    @test strictprecedes(DecoratedInterval(Interval(3.0, 4.0), def), nai()) == false
+    @test strictprecedes(nai(), DecoratedInterval(∅, trv)) == false
+    @test strictprecedes(nai(), nai()) == false
+    @test strictprecedes(DecoratedInterval(∅, trv), DecoratedInterval(Interval(3.0, 4.0), trv))
+    @test strictprecedes(DecoratedInterval(Interval(3.0, 4.0), def), DecoratedInterval(∅, trv))
+    @test strictprecedes(DecoratedInterval(∅, trv), DecoratedInterval(∅, trv))
+    @test strictprecedes(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test strictprecedes(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(1.0, 2.0), trv)) == false
+    @test strictprecedes(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test strictprecedes(DecoratedInterval(Interval(1.0, 2.0), trv), DecoratedInterval(Interval(3.0, 4.0), trv))
+    @test strictprecedes(DecoratedInterval(Interval(1.0, 3.0), def), DecoratedInterval(Interval(3.0, 4.0), trv)) == false
+    @test strictprecedes(DecoratedInterval(Interval(-3.0, -1.0), trv), DecoratedInterval(Interval(-1.0, 0.0), def)) == false
+    @test strictprecedes(DecoratedInterval(Interval(-3.0, -0.0), def), DecoratedInterval(Interval(0.0, 1.0), trv)) == false
+    @test strictprecedes(DecoratedInterval(Interval(-3.0, 0.0), trv), DecoratedInterval(Interval(-0.0, 1.0), trv)) == false
+    @test strictprecedes(DecoratedInterval(Interval(1.0, 3.5), trv), DecoratedInterval(Interval(3.0, 4.0), trv)) == false
+    @test strictprecedes(DecoratedInterval(Interval(1.0, 4.0), trv), DecoratedInterval(Interval(3.0, 4.0), def)) == false
+    @test strictprecedes(DecoratedInterval(Interval(-3.0, -0.1), trv), DecoratedInterval(Interval(-1.0, 0.0), trv)) == false
+end
+
+@testset "minimal_disjoint_test" begin
+    @test isdisjoint(∅, Interval(3.0, 4.0))
+    @test isdisjoint(Interval(3.0, 4.0), ∅)
+    @test isdisjoint(∅, ∅)
+    @test isdisjoint(Interval(3.0, 4.0), Interval(1.0, 2.0))
+    @test isdisjoint(Interval(0.0, 0.0), Interval(-0.0, -0.0)) == false
+    @test isdisjoint(Interval(0.0, -0.0), Interval(-0.0, 0.0)) == false
+    @test isdisjoint(Interval(3.0, 4.0), Interval(1.0, 7.0)) == false
+    @test isdisjoint(Interval(3.0, 4.0), Interval(-Inf, Inf)) == false
+    @test isdisjoint(Interval(-Inf, Inf), Interval(1.0, 7.0)) == false
+    @test isdisjoint(Interval(-Inf, Inf), Interval(-Inf, Inf)) == false
+end
+
+@testset "minimal_disjoint_dec_test" begin
+    @test isdisjoint(nai(), DecoratedInterval(Interval(3.0, 4.0), def)) == false
+    @test isdisjoint(DecoratedInterval(Interval(3.0, 4.0), trv), nai()) == false
+    @test isdisjoint(DecoratedInterval(∅, trv), nai()) == false
+    @test isdisjoint(nai(), nai()) == false
+    @test isdisjoint(DecoratedInterval(∅, trv), DecoratedInterval(Interval(3.0, 4.0), def))
+    @test isdisjoint(DecoratedInterval(Interval(3.0, 4.0), trv), DecoratedInterval(∅, trv))
+    @test isdisjoint(DecoratedInterval(∅, trv), DecoratedInterval(∅, trv))
+    @test isdisjoint(DecoratedInterval(Interval(3.0, 4.0), trv), DecoratedInterval(Interval(1.0, 2.0), def))
+    @test isdisjoint(DecoratedInterval(Interval(0.0, 0.0), trv), DecoratedInterval(Interval(-0.0, -0.0), trv)) == false
+    @test isdisjoint(DecoratedInterval(Interval(0.0, -0.0), trv), DecoratedInterval(Interval(-0.0, 0.0), trv)) == false
+    @test isdisjoint(DecoratedInterval(Interval(3.0, 4.0), def), DecoratedInterval(Interval(1.0, 7.0), def)) == false
+    @test isdisjoint(DecoratedInterval(Interval(3.0, 4.0), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+    @test isdisjoint(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(1.0, 7.0), trv)) == false
+    @test isdisjoint(DecoratedInterval(Interval(-Inf, Inf), trv), DecoratedInterval(Interval(-Inf, Inf), trv)) == false
+end
+# FactCheck.exitstatus()