Fix positive_eq_hull_preimage_singleton and move homogenize_top - #84
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The equality `f.positive = hull R (f ⁻¹' {c})` was false as stated: it fails
for `c < 0` (the hull lies on the nonpositive side of `f`) and over semirings
without division (`R = ℕ`, `f = id`, `c = 2`). It is now stated with `0 < c`
over linearly ordered fields and proven. The inequality direction
`hull_le_positive_of_subset_preimage_singleton` keeps its original generality
with `0 < c` and a direct proof.
`homogenize_top` relied on the false equality and is itself false over general
ordered rings (`R = ℤ[ε]`); it moves to the `Field` section, now proven.
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Not sure how the false statement became part of that file, likely a botched generalisation or something? |
YaelDillies
reviewed
Sep 2, 2026
…ion.lean Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
YaelDillies
approved these changes
Sep 3, 2026
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The equality
f.positive = hull R (f ⁻¹' {c})was false as stated: it fails forc < 0(the hull lies on the nonpositive side off) and over semirings without division (R = ℕ,f = id,c = 2). It is now stated with0 < cover linearly ordered fields and proven. The inequality directionhull_le_positive_of_subset_preimage_singletonkeeps its original generality with0 < cand a direct proof.homogenize_toprelied on the false equality and is itself false over general ordered rings (R = ℤ[ε]); it moves to theFieldsection, now proven.