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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).
\EXAMPLE
{
# let th1 = TAUT `p ==> p \/ q`
and th2 = ASSUME `p:bool`;;
val th1 : thm = |- p ==> p \/ q
val th2 : thm = p |- p
# MP th1 th2;;
val it : thm = p |- p \/ q
}
\SEEALSO
EQ_MP, MATCH_MP, MATCH_MP_TAC, MP_TAC.
\ENDDOC
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