 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)
  DISJ_RESQ_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)
 