PEXISTS_IMP_CONV : conv

- STRUCTURE
- LIBRARY
- pair
- SYNOPSIS
- Moves a paired existential quantification inwards through an implication.
- DESCRIPTION
- When applied to a term of the form ?p. t ==> u, where variables from p are not free in both t and u, PEXISTS_IMP_CONV returns a theorem of one of three forms, depending on occurrences of variable from p in t and u. If variables from p are free in t but none are in u, then the theorem:is returned. If variables from p are free in u but none are in t, then the result is:
|- (?p. t ==> u) = (!p. t) ==> u

And if no variable from p is free in either t nor u, then the result is:|- (?p. t ==> u) = t ==> (?p. u)

|- (?p. t ==> u) = (!p. t) ==> (?p. u)

- FAILURE
- PEXISTS_IMP_CONV fails if it is applied to a term not of the form ?p. t ==> u, or if it is applied to a term ?p. t ==> u in which the variables from p are free in both t and u.
- SEEALSO

HOL Kananaskis-14