\DOC SUBS_OCCS
\TYPE {SUBS_OCCS : (int list * thm) list -> thm -> thm}
\SYNOPSIS
Makes substitutions in a theorem at specific occurrences of a term, using
a
list of equational theorems.
\KEYWORDS
rule.
\DESCRIBE
Given a list {(l1,A1|-t1=v1),...,(ln,An|-tn=vn)} and a theorem
{(A|-t)}, {SUBS_OCCS} simultaneously replaces each {ti} in {t} with {vi},
at the occurrences specified by the integers
in the list {li = [o1,...,ok]} for each theorem {Ai|-ti=vi}.
{
(l1,A1|-t1=v1) ... (ln,An|-tn=vn) A|-t
------------------------------------------- SUBS_OCCS[(l1,A1|t1=v1),...,
A1 u ... An u A |- t[v1,...,vn/t1,...,tn]
(ln,An|-tn=vn)]
(A|-t)
}
\FAILURE
{SUBS_OCCS [(l1,th1),...,(ln,thn)] (A|-t)} fails
the conclusion of any theorem in the list is not
No change is made to the theorem if the supplied
left-hand side of the conclusion of {thi} do not
if
an equation.
occurrences {li} of the
appear in {t}.
\EXAMPLE
The commutative law for addition
{
- val thm = SPECL [Term `m:num`, Term`n:num`]
arithmeticTheory.ADD_SYM;
> val thm = |- m + n = n + m : thm
}
can be used for substituting only the second occurrence of
the subterm {m + n}
{
- SUBS_OCCS [([2],thm)]
(ASSUME (Term `(n + m) + (m + n) = (m + n) + (m + n)`));
> val it = [.] |- n + m + (m + n) = n + m + (m + n) : thm
}
\USES
{SUBS_OCCS} is used when rewriting at specific occurrences of a term, and
rules
such as {REWRITE_RULE}, {PURE_REWRITE_RULE}, {ONCE_REWRITE_RULE}, and
{SUBS}
are too extensive or would diverge.
\SEEALSO
Rewrite.ONCE_REWRITE_RULE, Rewrite.PURE_REWRITE_RULE,
Rewrite.REWRITE_RULE, Drule.SUBS, Thm.SUBST, Rewrite.SUBST_MATCH.
\ENDDOC