And Elimination
   
 

This rule can be used forwards to derive a subformula from an AND formula, or backwards to derive a new goal which is a conjunction of the current goal and some other formula.

In forwards mode this rule also allows you to eliminate multiple conjuncts in the top level formula (for e.g p^q^r^s^t^u to p,q,r,s,t,u), or you could skip so that smaller groups are formed from which you could eliminate the chosen sub formula.

To use it forwards:
  1. select an empty line and click on the And Elimination button.
  2. then select the AND formula line you wish to apply the rule to (this line must be in the scope of the empty line).
  3. when prompted, choose the side of the AND formula you want to derive (left,right or both) in the Dialog Box.
  4. the subformula you specified will then appear as a new line in your proof.

To use it backwards:
  1. select a goal line and click on the And Elimination.
  2. you will be prompted to choose whether the current goal should go on the left or right.
  3. you will then be prompted to type in the formula to appear on the other side of the conjunction. 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.