lean2/tests/lean/run/occurs_check_bug1.lean
Leonardo de Moura e51c4ad2e9 feat(frontends/lean): rename 'using' command to 'open'
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-09-03 16:00:38 -07:00

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import logic data.nat data.prod
open nat prod
open decidable
variable modulo (x : ) (y : ) :
infixl `mod`:70 := modulo
variable gcd_aux : ×
definition gcd (x y : ) : := gcd_aux (pair x y)
theorem gcd_def (x y : ) : gcd x y = @ite (y = 0) (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) :=
trans (gcd_def _ _) (if_neg succ_ne_zero)