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Replace AboveBelow lattice-axiom case bashes with aesop

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The six lattice axioms (sup/inf comm/assoc, absorption) all close with a
uniform `rcases <;> aesop`, removing the per-lemma simp-lemma lists that had
to be kept in sync with the Max/Min definitions.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
Danila Fedorin
2026-06-27 19:49:13 -05:00
parent 445187837c
commit 9e0702b5f5
1 changed files with 6 additions and 20 deletions
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26
lean/Spa/Lattice/AboveBelow.lean
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@@ -49,36 +49,22 @@ instance : Min (AboveBelow α) where
(mk x ⊓ mk y : AboveBelow α) = if x = y then mk x else bot := rfl
protected lemma sup_comm (a b : AboveBelow α) : a ⊔ b = b ⊔ a := by
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> simp only
[bot_sup, sup_bot, top_sup, sup_top, mk_sup_mk]
split_ifs with h₁ h₂ h₂ <;> simp_all
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> aesop
protected lemma sup_assoc (a b c : AboveBelow α) : a ⊔ b ⊔ c = a ⊔ (b ⊔ c) := by
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> rcases c with _ | _ | z <;>
simp only [bot_sup, sup_bot, top_sup, sup_top, mk_sup_mk]
split_ifs <;> simp_all
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> rcases c with _ | _ | z <;> aesop
protected lemma inf_comm (a b : AboveBelow α) : a ⊓ b = b ⊓ a := by
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> simp only
[bot_inf, inf_bot, top_inf, inf_top, mk_inf_mk]
split_ifs with h₁ h₂ h₂ <;> simp_all
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> aesop
protected lemma inf_assoc (a b c : AboveBelow α) : a ⊓ b ⊓ c = a ⊓ (b ⊓ c) := by
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> rcases c with _ | _ | z <;>
simp only [bot_inf, inf_bot, top_inf, inf_top, mk_inf_mk]
split_ifs <;> simp_all
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> rcases c with _ | _ | z <;> aesop
protected lemma sup_inf_self (a b : AboveBelow α) : a ⊔ a ⊓ b = a := by
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;>
simp only [bot_sup, sup_bot, top_sup, sup_top, mk_sup_mk,
bot_inf, inf_bot, top_inf, inf_top, mk_inf_mk] <;>
try (split_ifs <;> simp_all)
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> aesop
protected lemma inf_sup_self (a b : AboveBelow α) : a ⊓ (a ⊔ b) = a := by
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;>
simp only [bot_sup, sup_bot, top_sup, sup_top, mk_sup_mk,
bot_inf, inf_bot, top_inf, inf_top, mk_inf_mk] <;>
try (split_ifs <;> simp_all)
rcases a with _ | _ | x <;> rcases b with _ | _ | y <;> aesop
instance : Lattice (AboveBelow α) :=
Lattice.mk' AboveBelow.sup_comm AboveBelow.sup_assoc