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feat(Data/Fin): prove fflatten_embedSum and fflatten₂_embedSum #607

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alexanderlhicks merged 1 commit into from
Jul 7, 2026
+24 −2
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feat(Data/Fin): prove fflatten_embedSum and fflatten₂_embedSum #607

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26 changes: 24 additions & 2 deletions ArkLib/Data/Fin/Sigma.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -323,7 +323,18 @@ theorem fflatten_embedSum {A : Sort u} {F : A → Sort v} {m : ℕ} {n : Fin m
{α : (i : Fin m) → (j : Fin (n i)) → A}
(v : (i : Fin m) → (j : Fin (n i)) → F (α i j)) (i : Fin m) (j : Fin (n i)) :
fflatten v (embedSum i j) = cast (by simp) (v i j) := by
sorry
induction m with
| zero => exact Fin.elim0 i
| succ m ih =>
induction i using Fin.cases with
| zero =>
simp only [embedSum_succ_zero, fflatten_succ]
erw [fappend_left]
rfl
| succ i =>
simp only [embedSum_succ_succ, fflatten_succ]
erw [fappend_right, ih (fun i => v i.succ) i j, _root_.cast_cast]
rfl

/-- Functorial flatten with two arguments: flattens two nested heterogeneous tuple
`(i : Fin m) → (j : Fin (n i)) → F (α i j)` into a single heterogeneous tuple with type
Expand Down Expand Up @@ -380,7 +391,18 @@ theorem fflatten₂_embedSum {A : Sort u} {B : Sort v} {F : A → B → Sort w}
{β : (i : Fin m) → (j : Fin (n i)) → B}
(v : (i : Fin m) → (j : Fin (n i)) → F (α i j) (β i j)) (i : Fin m) (j : Fin (n i)) :
fflatten₂ v (embedSum i j) = cast (by simp) (v i j) := by
sorry
induction m with
| zero => exact Fin.elim0 i
| succ m ih =>
induction i using Fin.cases with
| zero =>
simp only [embedSum_succ_zero, fflatten₂_succ]
erw [fappend₂_left]
rfl
| succ i =>
simp only [embedSum_succ_succ, fflatten₂_succ]
erw [fappend₂_right, ih (fun i => v i.succ) i j, _root_.cast_cast]
rfl

/-- Heterogeneous flatten: flattens a nested heterogeneous tuple
`(i : Fin m) → (j : Fin (n i)) → α i j` into a single heterogeneous tuple with type
Expand Down
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