| Entry |
Value |
|
Name |
EVEN_ADD |
|
Conclusion |
!m n. EVEN (m + n) <=> EVEN m <=> EVEN n |
|
Constructive Proof |
No |
|
Axiom |
!t. t \/ ~t |
|
Classical Lemmas |
!t. ~ ~t <=> t!t. (t <=> T) \/ (t <=> F) |
|
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!t1 t2. t1 \/ t2 <=> t2 \/ t1!t. (!x. t) <=> t!t. ~ ~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!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 <=> t!t. t ==> t!t. (t <=> T) \/ (t <=> F)!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. m + SUC n = SUC (m + n)!m n. SUC m + n = SUC (m + n)!n. EVEN (SUC n) <=> ~EVEN n!n. ODD (SUC n) <=> ~ODD n!n. ~EVEN n <=> ODD n!n. ~ODD n <=> EVEN n!m. m + 0 = m!n. 0 + n = n!n. EVEN n \/ ODD nEVEN 0~ODD 0F <=> (!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)NUMERAL = (\n. n) |
|
Contained Package |
natural-div-thm |
|
Comment |
Standard HOL library retrieved from OpenTheory |
