EXISTS_AND_CONV : conv

- STRUCTURE
- SYNOPSIS
- Moves an existential quantification inwards through a conjunction.
- DESCRIPTION
- When applied to a term of the form ?x. P /\ Q, where x is not free in both P and Q, EXISTS_AND_CONV returns a theorem of one of three forms, depending on occurrences of the variable x in P and Q. If x is free in P but not in Q, then the theorem:is returned. If x is free in Q but not in P, then the result is:
|- (?x. P /\ Q) = (?x.P) /\ Q

And if x is free in neither P nor Q, then the result is:|- (?x. P /\ Q) = P /\ (?x.Q)

|- (?x. P /\ Q) = (?x.P) /\ (?x.Q)

- FAILURE
- EXISTS_AND_CONV fails if it is applied to a term not of the form ?x. P /\ Q, or if it is applied to a term ?x. P /\ Q in which the variable x is free in both P and Q.
- SEEALSO

HOL Kananaskis-14