File: MP.doc

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\DOC MP

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

\SYNOPSIS
Implements the Modus Ponens inference rule.

\KEYWORDS
rule, modus ponens, implication.

\DESCRIBE
When applied to theorems {A1 |- t1 ==> t2} and {A2 |- t1},
the inference rule {MP} returns the theorem {A1 u A2 |- t2}.
{
    A1 |- t1 ==> t2   A2 |- t1
   ----------------------------  MP
          A1 u A2 |- t2
}
\FAILURE
Fails unless the first theorem is an implication whose antecedent is the
same as the conclusion of the second theorem (up to alpha-conversion).

\SEEALSO
EQ_MP, LIST_MP, MATCH_MP, MATCH_MP_TAC, MP_TAC, NOT_MP.

\ENDDOC