For All Introduction
   
 

This rule can be applied forwards to derive a For All formula or applied backwards to a FOR ALL goal line.

To apply this rule:

  1. select both the empty and For All Introduction.
  2. enter the For All formula you wish to derive when prompted. This formula must not contain any predicate symbols, function symbols or constants that are not in the signature of the box you are working in.
  3. a new box is then added to the proof which declares a skolem constant (e.g. sk1) and has the FOR ALL formula's sub formula as a new goal with the variable replaced by the skolem constant and the For All formula after the box.
To use this rule backwards:
  1. select both the FOR ALL goal line to use and FOR ALL Introduction.
  2. a new box is then added to the proof which declares a skolem constant (e.g. sk1) and has the FOR ALL formula's sub formula as a new goal with the variable replaced by the skolem constant and the For All formula after the box.

(NOTE: This rule will deal with several FOR ALL at once.)