CCONTR

Thm.CCONTR : term -> thm -> thm

Implements the classical contradiction rule.

When applied to a term t and a theorem A |- F, the inference rule CCONTR returns the theorem A - {~t} |- t.

       A |- F
   ---------------  CCONTR t
    A - {~t} |- t

Failure

Fails unless the term has type bool and the theorem has F as its conclusion.

Comments

The usual use will be when ~t exists in the assumption list; in this case, CCONTR corresponds to the classical contradiction rule: if ~t leads to a contradiction, then t must be true.

See also

Drule.CONTR, Drule.CONTRAPOS, Tactic.CONTR_TAC, Thm.NOT_ELIM