EXISTS : term * term -> thm -> thm
Introduces existential quantification given a particular witness.
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
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.