\DOC SUBST_ALL_TAC
\TYPE {SUBST_ALL_TAC : thm_tactic}
\SYNOPSIS
Substitutes using a single equation in both the assumptions and conclusion of a goal.
\KEYWORDS tactic.
\DESCRIBE
{SUBST_ALL_TAC} breaches the style of natural deduction, where the assumptions are kept fixed. Given a theorem {A|-u=v} and a goal {([t1;...;tn], t)},
{SUBST_ALL_TAC (A|-u=v)} transforms the assumptions {t1},...,{tn} and the term
{t} into {t1[v/u]},...,{tn[v/u]} and {t[v/u]} respectively, by substituting {v} for each free occurrence of {u} in both the assumptions and the conclusion of the goal.
{
{t1,...,tn} ?- t
================================= SUBST_ALL_TAC (A|-u=v)
{t1[v/u],...,tn[v/u]} ?- t[v/u]
}
The assumptions of the theorem used to substitute with are not added to the assumptions of the goal, but they are recorded in the proof. If
{A} is not a subset of the assumptions of the goal (up to alpha-conversion), then
{SUBST_ALL_TAC (A|-u=v)} results in an invalid tactic.
{SUBST_ALL_TAC} automatically renames bound variables to prevent free variables in {v} becoming bound after substitution.
\FAILURE
{SUBST_ALL_TAC th (A,t)} fails if the conclusion of {th} is not an equation.
No change is made to the goal if no occurrence of the left-hand side of
{th} appears free in {(A,t)}.
\EXAMPLE
Simplifying both the assumption and the term in the goal
{
{0 + m = n} ?- 0 + (0 + m) = n
} by substituting with the theorem {|- 0 + m = m} for addition
{
SUBST_ALL_TAC (CONJUNCT1 ADD_CLAUSES)
} results in the goal
{
{m = n} ?- 0 + m = n
}
\SEEALSO

Rewrite.ONCE_REWRITE_TAC, Rewrite.PURE_REWRITE_TAC, Rewrite.REWRITE_TAC,
Tactic.SUBST1_TAC, Tactic.SUBST_TAC.
\ENDDOC