lean2/tests/lean/run/occurs_check_bug1.lean

17 lines
478 B
Text
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

import logic data.nat data.prod
open nat prod
open decidable
constant modulo (x : ) (y : ) :
infixl `mod` := modulo
constant gcd_aux : ×
definition gcd (x y : ) : := gcd_aux (pair x y)
theorem gcd_def (x y : ) : gcd x y = @ite (y = 0) (nat.has_decidable_eq (pr2 (pair x y)) 0) nat x (gcd y (x mod y)) :=
sorry
theorem gcd_succ (m n : ) : gcd m (succ n) = gcd (succ n) (m mod succ n) :=
eq.trans (gcd_def _ _) (if_neg !succ_ne_zero)