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Usw OrderBot / OrderTop for lattice witnesses

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Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Co-Authored-By: OpenAI Codex <codex@openai.com>
This commit is contained in:
Danila Fedorin
2026-06-26 14:49:57 -05:00
parent 6a6ed521ca
commit e738eb4294
5 changed files with 51 additions and 30 deletions
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5
lean/Spa/Fixedpoint.lean
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@@ -24,8 +24,7 @@ def doStep (f : α → α) (hf : Monotone f) :
def fix (f : α → α) (hf : Monotone f) : {a : α // a = f a} :=
doStep f hf (height (α := α) + 1) (RelSeries.singleton _ ⊥)
(by simp)
(by simpa [RelSeries.last_singleton]
using FiniteHeightLattice.bot_le α (f ⊥))
(by simp)
def aFix (f : α → α) (hf : Monotone f) : α :=
(fix f hf).1
@@ -50,7 +49,7 @@ lemma doStep_le (f : α → α) (hf : Monotone f)
theorem aFix_le (f : α → α) (hf : Monotone f)
{a : α} (ha : a = f a) : aFix f hf ≤ a :=
doStep_le f hf ha _ _ _ _ (by simpa using FiniteHeightLattice.bot_le α a)
doStep_le f hf ha _ _ _ _ (by simp)
end Fixedpoint