X_CHOOSE_TAC : term -> thm_tactic

- STRUCTURE
- SYNOPSIS
- Assumes a theorem, with existentially quantified variable replaced by a given witness.
- DESCRIPTION
- X_CHOOSE_TAC expects a variable y and theorem with an existentially quantified conclusion. When applied to a goal, it adds a new assumption obtained by introducing the variable y as a witness for the object x whose existence is asserted in the theorem.
A ?- t =================== X_CHOOSE_TAC y (A1 |- ?x. w) A u {w[y/x]} ?- t (y not free anywhere)

- FAILURE
- Fails if the theorem’s conclusion is not existentially quantified, or if the first argument is not a variable. Failures may arise in the tactic-generating function. An invalid tactic is produced if the introduced variable is free in w, t or A, or if the theorem has any hypothesis which is not alpha-convertible to an assumption of the goal.
- EXAMPLE
- Given a goal of the formthe following theorem may be applied:
{n < m} ?- ?x. m = n + (x + 1)

by the tactic (X_CHOOSE_TAC (Term`q:num`) th) giving the subgoal:th = [n < m] |- ?p. m = n + p

{n < m, m = n + q} ?- ?x. m = n + (x + 1)

- SEEALSO

HOL Kananaskis-14