63 lines
1.6 KiB
Text
63 lines
1.6 KiB
Text
open nat
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inductive vec (α : Type*) : ℕ → Type*
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| nil {} : vec 0
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| cons : α → Π {n : nat}, vec n → vec (n+1)
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namespace vec
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def head {α : Type*} : Π {n : ℕ}, vec α (n+1) → α
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| n (cons x xs) := x
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end vec
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constants (dret : Π {n : ℕ}, vec nat n → (vec nat n → nat) → nat)
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axiom dret_spec : Π {n : ℕ} (xs : vec nat n) (f : vec nat n → nat), dret xs f = f xs
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example (v : vec nat 1) : dret v vec.head = vec.head v :=
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by rw dret_spec
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example (v : vec nat 2) : dret v vec.head = vec.head v :=
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by rw dret_spec
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example (v : vec nat 3) : dret v vec.head = vec.head v :=
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by rw dret_spec
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example (v : vec nat 6) : dret v vec.head = vec.head v :=
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by rw dret_spec
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example (v : vec nat 32) : dret v vec.head = vec.head v :=
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by rw dret_spec
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example (v : vec nat 63) : dret v vec.head = vec.head v :=
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by rw dret_spec
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example (v : vec nat 64) : dret v vec.head = vec.head v :=
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by rw dret_spec
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example {n : nat} (v : vec nat (n+1)) : dret v vec.head = vec.head v :=
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by rw dret_spec
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example {n : nat} (v : vec nat (n+2)) : dret v vec.head = vec.head v :=
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by rw dret_spec
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example {n : nat} (v : vec nat (n+3)) : dret v vec.head = vec.head v :=
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by rw dret_spec
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attribute [simp] dret_spec
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example (v : vec nat 1) : dret v vec.head = vec.head v :=
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by simp
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example (v : vec nat 2) : dret v vec.head = vec.head v :=
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by simp
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example (v : vec nat 3) : dret v vec.head = vec.head v :=
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by simp
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example {n : nat} (v : vec nat (n+1)) : dret v vec.head = vec.head v :=
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by simp
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example {n : nat} (v : vec nat (n+2)) : dret v vec.head = vec.head v :=
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by simp
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example {n : nat} (v : vec nat (n+3)) : dret v vec.head = vec.head v :=
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by simp
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