Theory: boolarith2

Parents


Type constants


Term constants


Axioms


Definitions


Theorems

F_IMP_EX_F
|- F ==> (?t. F)
EX_F_IMP_F
|- (?t. F) ==> F
F_FROM_EX_F
|- (?t. F) = F
ID_IMP
|- !b. b ==> b
CONJ_IMP_TAUT
|- !a b c. (a ==> b) ==> a /\ c ==> b /\ c
CONJ2_IMP_TAUT
|- !a b c d. (a ==> b) ==> d /\ a /\ c ==> d /\ b /\ c
CONJ3_IMP_TAUT
|- !a b c. (a ==> b) ==> c /\ a ==> c /\ b
ADD_SUC_0
|- !m. SUC m = SUC 0 + m
LESS_MONO_MULT'
|- !p n m. m <= n ==> p * m <= p * n
LESS_EQ_0_N
|- !n. 0 <= n
LESS_EQ_MONO_ADD_EQ'
|- !p n m. m <= n = p + m <= p + n
LESS_EQ_MONO_ADD_EQ1
|- !p m. m + p <= p = m <= 0
LESS_EQ_MONO_ADD_EQ2
|- !n p. p <= n + p = 0 <= n
LESS_EQ_MONO_ADD_EQ3
|- !n p. p <= n + p
ADD_SYM_ASSOC
|- !a b c. a + b + c = b + a + c
NOT_SUC_LEQ_0
|- !n. ~(SUC n <= 0)
INV_SUC_LEQ
|- !m n. SUC m <= SUC n = m <= n
TWICE
|- !x. x + x = SUC (SUC 0) * x
NOT_SUC_LEQ
|- ~(!n m. SUC m <= n)
LEQ_SPLIT
|- m + n <= p ==> n <= p /\ m <= p