EQ_MP : thm -> thm -> thm
STRUCTURE
Thm
SYNOPSIS
Equality version of the Modus Ponens rule.
DESCRIPTION
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.
SEEALSO
EQ_IMP_RULE
,
IMP_ANTISYM_RULE
,
MP
HOL
Kananaskis-13