STRIP_ASSUME_TAC
Tactic.STRIP_ASSUME_TAC : thm_tactic
Splits a theorem into a list of theorems and then adds them to the assumptions.
Given a theorem th and a goal (A,t), STRIP_ASSUME_TAC th splits
th into a list of theorems. This is done by recursively breaking
conjunctions into separate conjuncts, cases-splitting disjunctions, and
eliminating existential quantifiers by choosing arbitrary variables.
Schematically, the following rules are applied:
A ?- t
====================== STRIP_ASSUME_TAC (A' |- v1 /\ ... /\ vn)
A u {v1,...,vn} ?- t
A ?- t
================================= STRIP_ASSUME_TAC (A' |- v1 \/ ... \/ vn)
A u {v1} ?- t ... A u {vn} ?- t
A ?- t
==================== STRIP_ASSUME_TAC (A' |- ?x.v)
A u {v[x'/x]} ?- t
where x' is a variant of x.
If the conclusion of th is not a conjunction, a disjunction or an
existentially quantified term, the whole theorem th is added to the
assumptions.
As assumptions are generated, they are examined to see if they solve the goal (either by being alpha-equivalent to the conclusion of the goal or by deriving a contradiction).
The assumptions of the theorem being split are not added to the
assumptions of the goal(s), but they are recorded in the proof. This
means that if A' is not a subset of the assumptions A of the goal
(up to alpha-conversion), STRIP_ASSUME_TAC (A'|-v) results in an
invalid tactic.
Failure
Never fails.
Example
When solving the goal
?- m = 0 + m
assuming the clauses for addition with STRIP_ASSUME_TAC ADD_CLAUSES
results in the goal
{m + (SUC n) = SUC(m + n), (SUC m) + n = SUC(m + n),
m + 0 = m, 0 + m = m, m = 0 + m} ?- m = 0 + m
while the same tactic directly solves the goal
?- 0 + m = m
STRIP_ASSUME_TAC is used when applying a previously proved theorem to
solve a goal, or when enriching its assumptions so that resolution,
rewriting with assumptions and other operations involving assumptions
have more to work with.
See also
Tactic.ASSUME_TAC,
Tactic.CHOOSE_TAC,
Thm_cont.CHOOSE_THEN,
Thm_cont.CONJUNCTS_THEN,
Tactic.DISJ_CASES_TAC,
Thm_cont.DISJ_CASES_THEN