8dec57987a
This PR adds additional tests for `grind`, demonstrating that we can automate some manual proofs from Mathlib's basic category theory library, with less reliance on Mathlib's `@[reassoc]` trick. In several places I've added bidirectional patterns for equational lemmas. I've updated some other files to use the new `@[grind_eq]` attribute (but left as is all cases where we are inspecting the info messages from `grind_pattern`). --------- Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
30 lines
1.1 KiB
Text
30 lines
1.1 KiB
Text
class One (α : Type u) where
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one : α
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instance (priority := 300) One.toOfNat1 {α} [One α] : OfNat α (nat_lit 1) where
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ofNat := ‹One α›.1
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class Shelf (α : Type u) where
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act : α → α → α
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self_distrib : ∀ {x y z : α}, act x (act y z) = act (act x y) (act x z)
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class UnitalShelf (α : Type u) extends Shelf α, One α where
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one_act : ∀ a : α, act 1 a = a
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act_one : ∀ a : α, act a 1 = a
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infixr:65 " ◃ " => Shelf.act
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-- Mathlib proof from UnitalShelf.act_act_self_eq
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example {S} [UnitalShelf S] (x y : S) : (x ◃ y) ◃ x = x ◃ y := by
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have h : (x ◃ y) ◃ x = (x ◃ y) ◃ (x ◃ 1) := by rw [UnitalShelf.act_one]
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rw [h, ← Shelf.self_distrib, UnitalShelf.act_one]
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attribute [grind =] UnitalShelf.one_act UnitalShelf.act_one
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-- We actually want the reverse direction of `Shelf.self_distrib`, so don't use the `grind_eq` attribute.
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grind_pattern Shelf.self_distrib => self.act (self.act x y) (self.act x z)
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-- Proof using `grind`:
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example {S} [UnitalShelf S] (x y : S) : (x ◃ y) ◃ x = x ◃ y := by
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have h : (x ◃ y) ◃ x = (x ◃ y) ◃ (x ◃ 1) := by grind
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grind
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