lean2/tests/lean/run/nat_bug4.lean
2014-08-20 18:04:31 -07:00

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Text

import standard
using num eq_ops
inductive nat : Type :=
| zero : nat
| succ : nat → nat
definition add (x y : nat) : nat := nat_rec x (λn r, succ r) y
infixl `+`:65 := add
definition mul (n m : nat) := nat_rec zero (fun m x, x + n) m
infixl `*`:75 := mul
axiom mul_succ_right (n m : nat) : n * succ m = n * m + n
theorem small2 (n m l : nat) : n * succ l + m = n * l + n + m
:= subst (mul_succ_right _ _) (refl (n * succ l + m))