\DOC SUBST_TAC
\TYPE {SUBST_TAC : (thm list -> tactic)}
\SYNOPSIS
Makes term substitutions in a goal using a list of theorems.
\KEYWORDS
tactic.
\DESCRIBE
Given a list of theorems {A1|-u1=v1,...,An|-un=vn} and a goal {(A,t)},
{SUBST_TAC} rewrites the term {t} into the term {t[v1,...,vn/u1,...,un]}
by
simultaneously substituting {vi} for each occurrence of {ui} in {t} with
{vi}:
{
A ?- t
============================= SUBST_TAC [A1|-u1=v1,...,An|-un=vn]
A ?- t[v1,...,vn/u1,...,un]
}
The assumptions of the theorems used to substitute with are not added
to the assumptions {A} of the goal, while they are recorded in the proof.
If
any {Ai} is not a subset of {A} (up to alpha-conversion), then
{SUBST_TAC [A1|-u1=v1,...,An|-un=vn]} results in an invalid tactic.
{SUBST_TAC} automatically renames bound variables to prevent free
variables in
{vi} becoming bound after substitution.
\FAILURE
{SUBST_TAC [th1,...,thn] (A,t)} fails if the conclusion of any theorem in
the
list is not an equation. No change is made to the goal if no occurrence
of the
left-hand side of the conclusion of {thi} appears in {t}.
\EXAMPLE
When trying to solve the goal
{
?- (n + 0) + (0 + m) = m + n
}
by substituting with the theorems
{
- val thm1 = SPEC_ALL arithmeticTheory.ADD_SYM
val thm2 = CONJUNCT1 arithmeticTheory.ADD_CLAUSES;
thm1 = |- m + n = n + m
thm2 = |- 0 + m = m
}
applying {SUBST_TAC [thm1, thm2]} results in the goal
{
?- (n + 0) + m = n + m
}
\USES
{SUBST_TAC} is used when rewriting (for example, with {REWRITE_TAC}) is
extensive or would diverge. Substituting is also much faster than
rewriting.
\SEEALSO
Rewrite.ONCE_REWRITE_TAC, Rewrite.PURE_REWRITE_TAC, Rewrite.REWRITE_TAC,
Tactic.SUBST1_TAC, Tactic.SUBST_ALL_TAC.
\ENDDOC