natural-bits

Entry	Value
Name	natural-bits_36
Conclusion	!b. bit_cons b 0 = bit_to_num b
Constructive Proof	Yes
Axiom	N\|A
Classical Lemmas	N\|A
Constructive Lemmas	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. (!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 !b. bit_cons b 0 = bit_to_num b !t. t ==> t !f y. (\x. f x) y = f y !p q. (!x. p x ==> q x) ==> (?x. p x) ==> (?x. q x) !p. p _0 /\ (!n. p n ==> p (SUC n)) ==> (!n. p n) !m n. SUC m * n = m * n + n !m n. m + SUC n = SUC (m + n) !m n. SUC m + n = SUC (m + n) !m. m * 0 = 0 !n. 0 * n = 0 !m. m + 0 = m !n. 0 + n = n 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 q. !r. (p ==> r) ==> (q ==> r) ==> r) (!) = (\p. p = (\x. T)) (?) = (\p. !q. (!x. p x ==> q) ==> q) NUMERAL = (\n. n)
Contained Package	natural-bits
Comment	Probability package from OpenTheory.