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Constructive Lemmas |
T!h t. ~NULL (CONS h t)!h t. HD (CONS h t) = h!h t. TL (CONS h t) = t!x. x = x!p1 p2 q1 q2. (p1 ==> p2) /\ (q1 ==> q2) ==> p1 /\ q1 ==> p2 /\ q2!p1 p2 q1 q2. (p1 ==> p2) /\ (q1 ==> q2) ==> p1 \/ q1 ==> p2 \/ q2!t. (F <=> t) <=> ~t!t. (T <=> t) <=> t!t. (t <=> F) <=> ~t!t. (t <=> T) <=> t!t. F ==> t <=> T!t. T ==> t <=> t!t. t ==> F <=> ~t!t. t ==> T <=> T!t. t ==> t!p q. (!x. p x ==> q x) ==> (?x. p x) ==> (?x. q x)!p. p [] /\ (!h t. p t ==> p (CONS h t)) ==> (!l. p l)NULL []F <=> (!p. p)T <=> (\p. p) = (\p. p)~F <=> T~T <=> F(~) = (\p. p ==> F)(/\) = (\p q. (\f. f p q) = (\f. f T T))(==>) = (\p q. p /\ q <=> p)(\/) = (\p q. !r. (p ==> r) ==> (q ==> r) ==> r)(!) = (\p. p = (\x. T))(?) = (\p. !q. (!x. p x ==> q) ==> q) |
