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Constructive Lemmas |
T!x y. x = y <=> y = x!x y. x = y ==> y = x!a. ?x. x = a!x. x = x!t1 t2 t3. (t1 /\ t2) /\ t3 <=> t1 /\ t2 /\ t3!t1 t2. t1 /\ t2 <=> t2 /\ t1!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!t. t ==> t!f y. (\x. f x) y = f y!p q. (!x. p x ==> q) <=> (?x. p x) ==> q!p q. (!x. p x /\ q x) <=> (!x. p x) /\ (!x. q x)!p. (?!x. p x) <=> (?x. !y. p y <=> x = y)!p. (?!x. p x) <=> (?x. p x) /\ (!x x'. p x /\ p x' ==> x = x')F <=> (!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)(?!) = (\p. (?) p /\ (!x y. p x /\ p y ==> x = y)) |
