\DOC SUBST1_TAC
\TYPE {SUBST1_TAC : thm_tactic}
\SYNOPSIS
Makes a simple term substitution in a goal using a single equational
theorem.
\KEYWORDS
tactic.
\DESCRIBE
Given a theorem {A'|-u=v} and a goal {(A,t)}, the tactic
{SUBST1_TAC (A'|-u=v)} rewrites the term {t} into {t[v/u]}, by
substituting
{v} for each free occurrence of {u} in {t}:
{
A ?- t
============= SUBST1_TAC (A'|-u=v)
A ?- t[v/u]
}
The assumptions of the theorem used to substitute with are not added
to the assumptions of the goal but are recorded in the proof. If {A'} is
not a
subset of the assumptions {A} of the goal (up to alpha-conversion), then
{SUBST1_TAC (A'|-u=v)} results in an invalid tactic.
{SUBST1_TAC} automatically renames bound variables to prevent free
variables in
{v} becoming bound after substitution.
\FAILURE
{SUBST1_TAC th (A,t)} fails if the conclusion of {th} is not an equation.
No change is made to the goal if no free occurrence of the left-hand side
of {th} appears in {t}.
\EXAMPLE
When trying to solve the goal
{
?- m * n = (n * (m - 1)) + n
}
substituting with the commutative law for multiplication
{
SUBST1_TAC (SPECL ["m:num"; "n:num"] MULT_SYM)
}
results in the goal
{
?- n * m = (n * (m - 1)) + n
}
\USES
{SUBST1_TAC} is used when rewriting with a single theorem using tactics
such as
{REWRITE_TAC} is too expensive or would diverge. Applying {SUBST1_TAC} is
also
much faster than using rewriting tactics.
\SEEALSO
Rewrite.ONCE_REWRITE_TAC, Rewrite.PURE_REWRITE_TAC, Rewrite.REWRITE_TAC,
Tactic.SUBST_ALL_TAC, Tactic.SUBST_TAC.
\ENDDOC