Theory: res_quan

Parents


Type constants


Term constants


Axioms


Definitions


Theorems

RESQ_FORALL_CONJ_DIST
|- !P Q R. (!i ::P. Q i /\ R i) = (!i ::P. Q i) /\ (!i ::P. R i)
RESQ_FORALL_DISJ_DIST
|- !P Q R. (!i ::(\i. P i \/ Q i). R i) = (!i ::P. R i) /\ (!i ::Q. R i)
RESQ_FORALL_UNIQUE
|- !P j. (!i ::($= j). P i) = P j
RESQ_FORALL_FORALL
|- !P R x. (!x. !i ::P. R i x) = (!i ::P. !x. R i x)
RESQ_FORALL_REORDER
|- !P Q R. (!i ::P. !j ::Q. R i j) = (!j ::Q. !i ::P. R i j)
RESQ_EXISTS_DISJ_DIST
|- !P Q R. (?i ::P. Q i \/ R i) = (?i ::P. Q i) \/ (?i ::P. R i)
RESQ_DISJ_EXISTS_DIST
|- !P Q R. (?i ::(\i. P i \/ Q i). R i) = (?i ::P. R i) \/ (?i ::Q. R i)
RESQ_EXISTS_UNIQUE
|- !P j. (?i ::($= j). P i) = P j
RESQ_EXISTS_REORDER
|- !P Q R. (?i ::P. ?j ::Q. R i j) = (?j ::Q. ?i ::P. R i j)