PEXISTS_IMP : (term -> thm -> thm)

- STRUCTURE
- LIBRARY
- pair
- SYNOPSIS
- Existentially quantifies both the antecedent and consequent of an implication.
- DESCRIPTION
- When applied to a paired structure of variables p and a theorem A |- t1 ==> t2, the inference rule PEXISTS_IMP returns the theorem A |- (?p. t1) ==> (?p. t2), provided no variable in p is free in the assumptions.
A |- t1 ==> t2 -------------------------- EXISTS_IMP "x" [where x is not free in A] A |- (?x.t1) ==> (?x.t2)

- FAILURE
- Fails if the theorem is not implicative, or if the term is not a paired structure of variables, of if any variable in the pair is free in the assumption list.
- SEEALSO

HOL Kananaskis-14