d76752ffb8
This PR teaches `grind` how to reduce `.ctorIdx` applied to constructors. It can also handle tasks like ``` xs ≍ Vec.cons x xs' → xs.ctorIdx = 1 ``` thanks to a `.ctorIdx.hinj` theorem (generated on demand).
34 lines
1.1 KiB
Text
34 lines
1.1 KiB
Text
inductive N : Type where | z : N | s : N → N
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/-- info: N.ctorIdx : N → Nat -/
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#guard_msgs in
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#check N.ctorIdx
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/-- info: N.ctorIdx.hinj (x x' : N) (x_eq : x = x') : x.ctorIdx = x'.ctorIdx -/
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#guard_msgs in
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#check N.ctorIdx.hinj
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inductive Vec (α : Type) : Nat → Type where
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| nil : Vec α 0
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| cons : {n : Nat} → α → Vec α n → Vec α (Nat.succ n)
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/--
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info: Vec.ctorIdx.hinj {α : Type} {a✝ : Nat} (x : Vec α a✝) {α' : Type} {a'✝ : Nat} (x' : Vec α' a'✝) (α_eq : α = α') :
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a✝ = a'✝ → ∀ (x_eq : x ≍ x'), x.ctorIdx = x'.ctorIdx
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-/
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#guard_msgs in
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#check Vec.ctorIdx.hinj
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inductive EvenVec (α : Type) : (n : Nat) → (n % 2 = 0) → Type where
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| nil : EvenVec α 0 (by rfl)
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| cons : α → EvenVec α n p → EvenVec α (n + 2) (by grind)
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-- NB: No HEq between the proof arguments (they are not needed)
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/--
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info: EvenVec.ctorIdx.hinj {α : Type} {n : Nat} {a✝ : n % 2 = 0} (x : EvenVec α n a✝) {α' : Type} {n' : Nat}
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{a'✝ : n' % 2 = 0} (x' : EvenVec α' n' a'✝) (α_eq : α = α') (n_eq : n = n') (x_eq : x ≍ x') : x.ctorIdx = x'.ctorIdx
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-/
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#guard_msgs in
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#check EvenVec.ctorIdx.hinj
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