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\DOC extend_basic_congs
\TYPE {extend_basic_congs : thm list -> unit}
\SYNOPSIS
Extends the set of congruence rules used by the simplifier.
\DESCRIBE
The HOL Light simplifier (as invoked by {SIMP_TAC} etc.) uses congruence rules
to determine how it uses context when descending through a term. These are
essentially theorems showing how to decompose one equality to a series of other
inequalities in context. A call to {extend_basic_congs thl} adds the congruence
rules in {thl} to the defaults.
\FAILURE
Never fails.
\EXAMPLE
By default, the simplifier uses context {p} when simplifying {q} within an
implication {p ==> q}. Some users would like the simplifier to do likewise for
a conjunction {p /\ q}, which is not done by default:
{
# SIMP_CONV[] `x = 1 /\ x < 2`;;
val it : thm = |- x = 1 /\ x < 2 <=> x = 1 /\ x < 2
}
\noindent You can make it do so with
{
# extend_basic_congs
[TAUT `(p <=> p') ==> (p' ==> (q <=> q')) ==> (p /\ q <=> p' /\ q')`];;
val it : unit = ()
}
\noindent as you can see:
{
# SIMP_CONV[] `x = 1 /\ x < 2`;;
val it : thm = |- x = 1 /\ x < 2 <=> x = 1 /\ 1 < 2
# SIMP_CONV[ARITH] `x = 1 /\ x < 2`;;
val it : thm = |- x = 1 /\ x < 2 <=> x = 1
}
\SEEALSO
basic_congs, set_basic_congs, SIMP_CONV, SIMP_RULE, SIMP_TAC.
\ENDDOC
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