Or Elimination
   
 

This rule is used to eliminate an OR formula from your proof by proving a goal which can be achieved if either the left sub formula or the right sub formula of the OR formula is true (arguing by cases). When used forwards the goal to be proved must be input and when used backwards the current goal is used. In both cases the OR formula selected to eliminate is split into two cases and both cases together justify the goal.

To use it forwards:
  1. select both the empty line and OR Elimination

  2. then select the OR formula you wish to use

  3. enter the formula you would like to prove by OR Elimination when prompted. (Note: The formula should contain only terms in the signature and if extra terms required you can add them using add signature in the options menu.)

  4. a double box will be added to your proof with the left and right hand boxes assuming the left and right hand sub formulas of your OR formula, respectively, and having the formula you input as their conclusions.

To use it backwards:
  1. select both the goal line you wish to derive and Or Elimination.

  2. then select the OR formula line (in the scope of the goal line) you wish to use to derive the goal.

  3. a double box will then be added to your proof with the left and right hand boxes assuming the left and right hand sub formulas of your OR formula, respectively, and having the goal line you selected as their conclusions.