File: EQ_IMP_RULE.doc

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\DOC EQ_IMP_RULE

\TYPE {EQ_IMP_RULE : (thm -> (thm # thm))}

\SYNOPSIS
Derives forward and backward implication from equality of boolean terms.

\KEYWORDS
rule, implication, equality.

\DESCRIBE
When applied to a theorem {A |- t1 = t2}, where {t1} and {t2} both have
type {bool}, the inference rule {EQ_IMP_RULE} returns the
theorems {A |- t1 ==> t2} and {A |- t2 ==> t1}.
{
              A |- t1 = t2
   -----------------------------------  EQ_IMP_RULE
    A |- t1 ==> t2     A |- t2 ==> t1
}
\FAILURE
Fails unless the conclusion of the given theorem is an equation between
boolean terms.

\SEEALSO
EQ_MP, EQ_TAC, IMP_ANTISYM_RULE.

\ENDDOC