SUBST_VAR_TAC : thm -> tactic
Use an equation to substitute ``safely'' in goal.
When applied to a theorem with an equational hypothesis A |- s = t, SUBST_
VAR_TAC has no effect if s and t are alpha-equivalent. Otherwise, if
either side of the equation is a variable not free in the other side, or a
constant, and the conclusion contains no free variables not free in some
assumption of the goal, then the theorem is used to replace that constant or
variable throughout the goal, assumptions and conclusions. If none of these
cases apply, or the conclusion is not even an equation, the application fails.
- FAILURE CONDITIONS
Fails if applied to a non-equation for which none of the cases above hold.
By some sequence like REPEAT(FIRST_X_ASSUM SUBST_VAR_TAC) one can use all
possible assumptions to substitute ``safely'', in the sense that it will not
change the provability status of the goal. This is sometimes a useful prelude
to other automatic techniques.
- SEE ALSO