- IMP_REFL_THM
-
|- !x. x ==> x
- IMP_TRANS_THM
-
|- !x y z. (x ==> y) /\ (y ==> z) ==> x ==> z
- PMI_REFL_THM
-
|- !x. x <== x
- PMI_TRANS_THM
-
|- !x y z. (x <== y) /\ (y <== z) ==> (x <== z)
- COND1_THM
-
|- !R A B C D. (!x. R x x) ==> (A ==> R B D) ==> R (A => B | C) (A => D | C)
- COND2_THM
-
|- !R A B C D. (!x. R x x) ==> (~A ==> R C D) ==> R (A => B | C) (A => B | D)
- BODY2_THM
-
|- !c f g r. (!v. (v = c) ==> r (f v) (g v)) ==> r (f c) (g c)
- LET_THM
-
|- !c f g r. (!v. (v = c) ==> r (f v) (g v)) ==> r (LET f c) (LET g c)
- CONJ1_THM
-
|- !A B C. (B ==> (A = C)) ==> (A /\ B = C /\ B)
- CONJ2_THM
-
|- !A B C. (A ==> (B = C)) ==> (A /\ B = A /\ C)
- IMP1_THM
-
|- !A B C. (~B ==> (A = C)) ==> (A ==> B = C ==> B)
- IMP2_THM
-
|- !A B C. (A ==> (B = C)) ==> (A ==> B = A ==> C)
- PM1_THM
-
|- !A B C. (B ==> (A = C)) ==> (A <== B = C <== B)
- PMI2_THM
-
|- !A B C. (~A ==> (B = C)) ==> (A <== B = A <== C)
- DISJ1_THM
-
|- !A B C. (~B ==> (A = C)) ==> (A \/ B = C \/ B)
- DISJ2_THM
-
|- !A B C. (~A ==> (B = C)) ==> (A \/ B = A \/ C)
- DNEG_THM
-
|- !t. ~~t = t
- NOT_DISJ_THM
-
|- !t1 t2. ~(A \/ B) = ~A /\ ~B
- NOT_IMP_THM
-
|- !t1 t2. ~(t1 ==> t2) = t1 /\ ~t2
- NOT_PMI_THM
-
|- !t1 t2. ~(t1 <== t2) = ~t1 /\ t2
- COND_ABF_THM
-
|- !t1 t2. (t1 => t2 | F) = t1 /\ t2
- COND_AFC_THM
-
|- !t1 t3. (t1 => F | t3) = ~t1 /\ t3
- IMP_CONJ1_THM
-
|- !A B C. (B ==> A ==> C) ==> A /\ B ==> C /\ B
- IMP_CONJ2_THM
-
|- !A B C. (A ==> B ==> C) ==> A /\ B ==> A /\ C
- IMP_IMP1_THM
-
|- !A B C. (~B ==> (A <== C)) ==> (A ==> B) ==> C ==> B
- IMP_IMP2_THM
-
|- !A B C. (A ==> B ==> C) ==> (A ==> B) ==> A ==> C
- IMP_PMI1_THM
-
|- !A B C. (B ==> A ==> C) ==> (A <== B) ==> (C <== B)
- IMP_PMI2_THM
-
|- !A B C. (~A ==> (B <== C)) ==> (A <== B) ==> (A <== C)
- IMP_DISJ1_THM
-
|- !A B C. (~B ==> A ==> C) ==> A \/ B ==> C \/ B
- IMP_DISJ2_THM
-
|- !A B C. (~A ==> B ==> C) ==> A \/ B ==> A \/ C
- IMP_NEG_THM
-
|- !A B. (A <== B) ==> ~A ==> ~B
- PMI_CONJ1_THM
-
|- !A B C. (B ==> (A <== C)) ==> (A /\ B <== C /\ B)
- PMI_CONJ2_THM
-
|- !A B C. (A ==> (B <== C)) ==> (A /\ B <== A /\ C)
- PMI_IMP1_THM
-
|- !A B C. (~B ==> A ==> C) ==> ((A ==> B) <== (C ==> B))
- PMI_IMP2_THM
-
|- !A B C. (A ==> (B <== C)) ==> ((A ==> B) <== (A ==> C))
- PMI_PMI1_THM
-
|- !A B C. (B ==> (A <== C)) ==> ((A <== B) <== C <== B)
- PMI_PMI2_THM
-
|- !A B C. (~A ==> B ==> C) ==> ((A <== B) <== A <== C)
- PMI_DISJ1_THM
-
|- !A B C. (~B ==> (A <== C)) ==> (A \/ B <== C \/ B)
- PMI_DISJ2_THM
-
|- !A B C. (~A ==> (B <== C)) ==> (A \/ B <== A \/ C)
- PMI_NEG_THM
-
|- !A B. (A ==> B) ==> (~A <== ~B)