0173444d24
This PR implements heterogeneous contructor injectivity in `grind`. Example: ```lean opaque double : Nat → Nat inductive Parity : Nat -> Type | even (n) : Parity (double n) | odd (n) : Parity (Nat.succ (double n)) opaque q : Nat → Nat → Prop axiom qax : q a b → double a = double b attribute [grind →] qax example (motive : (x : Nat) → Parity x → Sort u_1) (h_2 : (j : Nat) → motive (double j) (Parity.even j)) (j n : Nat) (heq_1 : q j n) -- Implies that `double j = double n` (heq_2 : Parity.even n ≍ Parity.even j): h_2 n ≍ h_2 j := by grind ``` Closes #11449
52 lines
1.6 KiB
Text
52 lines
1.6 KiB
Text
opaque double : Nat → Nat
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def P (n : Nat) : Prop := n >= 0
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theorem pax (n : Nat) : P n := by grind [P]
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def T (n : Nat) : Type := Vector Nat n
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inductive Foo' (α β : Type u) : (n : Nat) → P n -> Type u
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| even (a : α) (n : Nat) (v : T n) (h : P n) : Foo' α β (double n) (pax _)
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| odd (b : β) (n : Nat) (v : T n) : Foo' α β (Nat.succ (double n)) (pax _)
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example (α β : Type) (a₁ a₂ : α)
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(n₁ n₂ : Nat)
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(v₁ : T n₁) (v₂ : T n₂)
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(h₁ : P n₁) (h₂ : P n₂)
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(h_1 : double n₁ = double n₂)
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(h_2 : Foo'.even (β := β) a₁ n₁ v₁ h₁ ≍ Foo'.even (β := β) a₂ n₂ v₂ h₂) :
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a₁ = a₂ ∧ n₁ = n₂ ∧ v₁ ≍ v₂ ∧ h₁ ≍ h₂ := by
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grind
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example (α β : Type) (a : α) (b : β)
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(n₁ n₂ : Nat)
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(v₁ : T n₁) (v₂ : T n₂)
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(h₁ : P n₁)
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(h_1 : double n₁ = (double n₂).succ)
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(h_2 : Foo'.even (β := β) a n₁ v₁ h₁ ≍ Foo'.odd (α := α) b n₂ v₂)
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: False := by
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grind
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inductive Parity : Nat -> Type
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| even (n) : Parity (double n)
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| odd (n) : Parity (Nat.succ (double n))
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example
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(motive : (x : Nat) → Parity x → Sort u_1)
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(h_2 : (j : Nat) → motive (double j) (Parity.even j))
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(j n : Nat)
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(heq_1 : double n = double j)
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(heq_2 : Parity.even n ≍ Parity.even j):
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h_2 n ≍ h_2 j := by
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grind
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opaque q : Nat → Nat → Prop
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axiom qax : q a b → double a = double b
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attribute [grind →] qax
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example
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(motive : (x : Nat) → Parity x → Sort u_1)
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(h_2 : (j : Nat) → motive (double j) (Parity.even j))
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(j n : Nat)
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(heq_1 : q j n)
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(heq_2 : Parity.even n ≍ Parity.even j):
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h_2 n ≍ h_2 j := by
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grind
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