\DOC CONTR

\TYPE {CONTR : term -> thm -> thm}

\SYNOPSIS
Implements the intuitionistic contradiction rule.

\KEYWORDS
rule, contradiction.

\DESCRIBE
When applied to a term {t} and a theorem {A |- F}, the inference rule {CONTR}
returns the theorem {A |- t}.
{
    A |- F
   --------  CONTR `t`
    A |- t
}

\FAILURE
Fails unless the term has type {bool} and the theorem has {F} as its
conclusion.

\EXAMPLE
{
  # let th = REWRITE_RULE[ARITH] (ASSUME `1 = 0`);;
  val th : thm = 1 = 0 |- F

  # CONTR `Russell:Person = Pope` th;;
  val it : thm = 1 = 0 |- Russell = Pope
}

\SEEALSO
CCONTR, CONTR_TAC, NOT_ELIM.

\ENDDOC