HINT_EXISTS_TAC : tactic

- STRUCTURE
- SYNOPSIS
- Reduces an existentially quantified goal by finding a witness which, from the assumption list, satisfies at least partially the body of the existential.
- DESCRIPTION
- 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:is turned by HINT_EXISTS_TAC into:
b = 0, a < 1, c > 0 ?- ?x. x < 1

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:

is turned by HINT_EXISTS_TAC into:b = 0, a < 1, c > 0 ?- ?x. x < 1 /\ x + x = c

b = 0, a < 1, c > 0 ?- a < 1 /\ a + a = c

- The location of the conjunct does not matter, the goal:

is turned by HINT_EXISTS_TAC into:b = 0, a < 1, c > 0 ?- ?x. x + x = c /\ x < 1

b = 0, a < 1, c > 0 ?- a + a = c /\ a < 1

- It can be convenient to chain the call to HINT_EXISTS_TAC with one to ASM_REWRITE_TAC in order to remove automatically the satisfied conjunct:

is turned by HINT_EXISTS_TAC THEN ASM_REWRITE_TAC[] into:b = 0, a < 1, c > 0 ?- ?x. x + x = c /\ x < 1

b = 0, a < 1, c > 0 ?- a + a = c

- USES
- Avoid providing a witness explicitly, in order to make the tactic script less fragile.
- SEEALSO

HOL Kananaskis-14