EXISTS : term * term -> thm -> thm

SYNOPSIS

Introduces existential quantification given a particular witness.

DESCRIPTION

When applied to a pair of terms and a theorem, the first term an existentially quantified pattern indicating the desired form of the result, and the second a witness whose substitution for the quantified variable gives a term which is the same as the conclusion of the theorem, EXISTS gives the desired theorem.

    A |- p[u/x]
   -------------  EXISTS (`?x. p`,`u`)
    A |- ?x. p

FAILURE CONDITIONS

Fails unless the substituted pattern is the same as the conclusion of the theorem.

EXAMPLE

The following examples illustrate how it is possible to deduce different things from the same theorem:

  # EXISTS (`?x. x <=> T`,`T`) (REFL `T`);;
  val it : thm = |- ?x. x <=> T

  # EXISTS (`?x:bool. x = x`,`T`) (REFL `T`);;
  val it : thm = |- ?x. x <=> x

SEE ALSO

CHOOSE, EXISTS_TAC, SIMPLE_EXISTS.