SUBST_OCCS_TAC

Tactic.SUBST_OCCS_TAC : (int list * thm) list -> tactic

Makes substitutions in a goal at specific occurrences of a term, using a list of theorems.

Given a list (l1,A1|-t1=u1),...,(ln,An|-tn=un) and a goal (A,t), SUBST_OCCS_TAC replaces each ti in t with ui, simultaneously, at the occurrences specified by the integers in the list li = [o1,...,ok] for each theorem Ai|-ti=ui.

              A ?- t
   =============================  SUBST_OCCS_TAC [(l1,A1|-t1=u1),...,
    A ?- t[u1,...,un/t1,...,tn]                   (ln,An|-tn=un)]

The assumptions of the theorems used to substitute with are not added to the assumptions A of the goal, but they are recorded in the proof. If any Ai is not a subset of A (up to alpha-conversion), SUBST_OCCS_TAC [(l1,A1|-t1=u1),...,(ln,An|-tn=un)] results in an invalid tactic.

SUBST_OCCS_TAC automatically renames bound variables to prevent free variables in ui becoming bound after substitution.

Failure

SUBST_OCCS_TAC [(l1,th1),...,(ln,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 the supplied occurrences li of the left-hand side of the conclusion of thi do not appear in t.

Example

When trying to solve the goal

   ?- (m + n) + (n + m) = (m + n) + (m + n)

applying the commutative law for addition on the third occurrence of the subterm m + n

   SUBST_OCCS_TAC [([3], SPECL [Term `m:num`, Term `n:num`]
                               arithmeticTheory.ADD_SYM)]

results in the goal

   ?- (m + n) + (n + m) = (m + n) + (n + m)

SUBST_OCCS_TAC is used when rewriting a goal at specific occurrences of a term, and when rewriting tactics such as REWRITE_TAC, PURE_REWRITE_TAC, ONCE_REWRITE_TAC, SUBST_TAC, etc. are too extensive or would diverge.

See also

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