lean2/tests/lean/unfold_rec.lean

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import data.examples.vector
open nat vector
variables {A B : Type}
variable {n : nat}
theorem tst1 : ∀ n m, succ n + succ m = succ (succ (n + m)) :=
begin
intro n m,
state,
rewrite [succ_add]
end
definition add2 (x y : nat) : nat :=
nat.rec_on x (λ y, y) (λ x r y, succ (r y)) y
local infix + := add2
theorem tst2 : ∀ n m, succ n + succ m = succ (succ (n + m)) :=
begin
intro n m,
esimp [add2],
state,
apply sorry
end
definition fib (A : Type) : nat → nat → nat → nat
| b 0 c := b
| b 1 c := c
| b (succ (succ a)) c := fib b a c + fib b (succ a) c
theorem fibgt0 : ∀ b n c, fib nat b n c > 0
| b 0 c := sorry
| b 1 c := sorry
| b (succ (succ m)) c :=
begin
unfold fib,
state,
apply sorry
end
theorem unzip_zip : ∀ {n : nat} (v₁ : vector A n) (v₂ : vector B n), unzip (zip v₁ v₂) = (v₁, v₂)
| 0 [] [] := rfl
| (succ m) (a::va) (b::vb) :=
begin
unfold [zip, unzip],
state,
rewrite [unzip_zip]
end