Theory: boolarith1

Parents


Type constants


Term constants


Axioms


Definitions


Theorems

NOT_EQ
|- !t1 t2. (t1 = t2) = ~t1 = ~t2
DISJ_ASSOC
|- !t1 t2 t3. t1 \/ t2 \/ t3 = (t1 \/ t2) \/ t3
LEFT_CONJ_DISTRIB
|- !t1 t2 t3. t1 /\ (t2 \/ t3) = t1 /\ t2 \/ t1 /\ t3
RIGHT_CONJ_DISTRIB
|- !t1 t2 t3. (t2 \/ t3) /\ t1 = t2 /\ t1 \/ t3 /\ t1
LEFT_DISJ_DISTRIB
|- !t1 t2 t3. t1 \/ t2 /\ t3 = (t1 \/ t2) /\ (t1 \/ t3)
RIGHT_DISJ_DISTRIB
|- !t1 t2 t3. t2 /\ t3 \/ t1 = (t2 \/ t1) /\ (t3 \/ t1)
LEFT_DISJ_CONJ
|- !a b. a /\ b \/ b = b
GREATER_EQ
|- !a b. a >= b = b <= a
NOT_LEQ
|- !a b. ~(a <= b) = b < a
EQ_LEQ
|- !a b. (a = b) = a <= b /\ b <= a
NOT_EQ_LEQ
|- !a b. ~(a = b) = a < b \/ b < a
LESS_LESSEQ
|- !a b. a < b = a + 1 <= b