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Constructive Lemmas |
T!x y. ~emptyr x y!x. ~(x IN {})!x. x = x!t. (!x. t) <=> t!t. (F <=> t) <=> ~t!t. (T <=> t) <=> t!t. (t <=> F) <=> ~t!t. (t <=> T) <=> t!f y. (\x. f x) y = f y!p a. (?x. a = x /\ p x) <=> p a!p x. x IN GSPEC p <=> p x!p x. x IN {y | p y} <=> p x!r. irreflexive r <=> (!x. ~r x x)!s x y. set_to_relation s x y <=> x,y IN sF <=> (!p. p)T <=> (\p. p) = (\p. p)~F <=> T~T <=> Femptyr = set_to_relation {}(~) = (\p. p ==> F)(/\) = (\p q. (\f. f p q) = (\f. f T T))(==>) = (\p q. p /\ q <=> p)(!) = (\p. p = (\x. T))(?) = (\p. !q. (!x. p x ==> q) ==> q){} = {x | F} |
