Law of Excluded Middle (EM)
   
 

This rule can be used forwards to introduce a formula of the form A | ~A into your proof or backwards to justify a line of the form A | ~A.

To use it forwards:

  1. select both an empty line and EM.
  2. when prompted enter the formula you wish to represent A in A | ~A. This formula must only contain predicate symbols, function symbols or constants in the empty line's signature.
  3. the formula A | ~A will then be added to your proof where A is the formula you entered.
  4. If you enter a negated formula ~B then ~B | B would be added to your proof.

To use it backwards:

  1. select both a goal line of the form A | ~A and EM.
  2. the formula will then be justified and the box containing the line will be closed (the empty line is removed and the box will turn green).