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

- STRUCTURE
- SYNOPSIS
- Makes substitutions in a goal at specific occurrences of a term, using a list of theorems.
- DESCRIPTION
- 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.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.
A ?- t ============================= SUBST_OCCS_TAC [(l1,A1|-t1=u1),..., A ?- t[u1,...,un/t1,...,tn] (ln,An|-tn=un)]

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 goalapplying the commutative law for addition on the third occurrence of the subterm m + n
?- (m + n) + (n + m) = (m + n) + (m + n)

results in the goalSUBST_OCCS_TAC [([3], SPECL [Term `m:num`, Term `n:num`] arithmeticTheory.ADD_SYM)]

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

- USES
- 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.
- SEEALSO

HOL Kananaskis-14