16 lines
419 B
Text
16 lines
419 B
Text
namespace experiment
|
|
inductive nat : Type
|
|
| zero : nat
|
|
| succ : nat → nat
|
|
|
|
namespace nat
|
|
definition add (x y : nat) : nat := nat.rec x (λn r, succ r) y
|
|
infixl `+` := add
|
|
|
|
axiom add_right_comm (n m k : nat) : n + m + k = n + k + m
|
|
open eq
|
|
#print "==========================="
|
|
theorem bug (a b c d : nat) : a + b + c + d = a + c + b + d
|
|
:= subst (add_right_comm a b c) (eq.refl (a + b + c + d))
|
|
end nat
|
|
end experiment
|