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Constructive Lemmas |
T!x. x = x!y s f. y IN IMAGE f s <=> (?x. y = f x /\ x IN s)!t1 t2. t1 /\ t2 <=> t2 /\ t1!t. (!x. t) <=> t!t. F /\ t <=> F!t. T /\ t <=> t!t. t /\ F <=> F!t. t /\ T <=> t!t. t /\ 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!f s. IMAGE f s = {y | ?x. x IN s /\ y = f x}!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 xF <=> (!p. p)T <=> (\p. p) = (\p. p)(~) = (\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) |
