File: CONTRAPOS.doc

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\DOC CONTRAPOS

\TYPE {CONTRAPOS : (thm -> thm)}

\SYNOPSIS
Deduces the contrapositive of an implication.

\KEYWORDS
rule, contrapositive, implication.

\DESCRIBE
When applied to a theorem {A |- s ==> t}, the inference rule {CONTRAPOS}
returns its contrapositive, {A |- ~t ==> ~s}.
{
     A |- s ==> t
   ----------------  CONTRAPOS
    A |- ~t ==> ~s
}
\FAILURE
Fails unless the theorem is an implication.

\SEEALSO
CCONTR, CONTR, CONTRAPOS_CONV, NOT_ELIM.

\ENDDOC