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\DOC EQ_MP
\TYPE {EQ_MP : thm -> thm -> thm}
\SYNOPSIS
Equality version of the Modus Ponens rule.
\KEYWORDS
rule, equality, modus, ponens.
\DESCRIBE
When applied to theorems {A1 |- t1 <=> t2} and {A2 |- t1}, the inference
rule {EQ_MP} returns the theorem {A1 u A2 |- t2}.
{
A1 |- t1 <=> t2 A2 |- t1
---------------------------- EQ_MP
A1 u A2 |- t2
}
\FAILURE
Fails unless the first theorem is equational and its left side
is the same as the conclusion of the second theorem (and is therefore
of type {bool}), up to alpha-conversion.
\EXAMPLE
{
# let th1 = SPECL [`p:bool`; `q:bool`] CONJ_SYM
and th2 = ASSUME `p /\ q`;;
val th1 : thm = |- p /\ q <=> q /\ p
val th2 : thm = p /\ q |- p /\ q
# EQ_MP th1 th2;;
val it : thm = p /\ q |- q /\ p
}
\COMMENTS
This is one of HOL Light's 10 primitive inference rules.
\SEEALSO
EQ_IMP_RULE, IMP_ANTISYM_RULE, MP, PROVE_HYP.
\ENDDOC
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