HINT_EXISTS_TAC
Tactic.HINT_EXISTS_TAC : tactic
Reduces an existentially quantified goal by finding a witness which, from the assumption list, satisfies at least partially the body of the existential.
When applied to a goal ?x. t1 /\ ... /\ tn, the tactic
HINT_EXISTS_TAC looks for an assumption of the form ti[u/x], where
i belongs to 1..n, and reduces the goal by taking u as a witness
for x.
Failure
Fails unless the goal contains an assumption of the expected form.
Example
-
The goal:
b = 0, a < 1, c > 0 ?- ?x. x < 1
is turned by HINT_EXISTS_TAC into:
b = 0, a < 1, c > 0 ?- a < 1
-
However the tactic also allows to make progress if only one conjunct of the existential is satisfied. For instance, the goal:
b = 0, a < 1, c > 0 ?- ?x. x < 1 /\ x + x = c
is turned by HINT_EXISTS_TAC into:
b = 0, a < 1, c > 0 ?- a < 1 /\ a + a = c
-
The location of the conjunct does not matter, the goal:
b = 0, a < 1, c > 0 ?- ?x. x + x = c /\ x < 1
is turned by HINT_EXISTS_TAC into:
b = 0, a < 1, c > 0 ?- a + a = c /\ a < 1
-
It can be convenient to chain the call to
HINT_EXISTS_TACwith one toASM_REWRITE_TACin order to remove automatically the satisfied conjunct:b = 0, a < 1, c > 0 ?- ?x. x + x = c /\ x < 1
is turned by HINT_EXISTS_TAC THEN ASM_REWRITE_TAC[] into:
b = 0, a < 1, c > 0 ?- a + a = c
Avoid providing a witness explicitly, in order to make the tactic script less fragile.