This rule is can be used forwards to derive bottom from two contradictory lines or backwards to obtain a contradictory goal line from a bottom goal line and another formula.
Note: Bottom Introduction is the same rule as Not Elimination
To use it forwards:
- select an empty line and click on Not Elimination
- then select the two contradictory lines (for example a and ~a). These lines must be in scope and one of the lines must be a not formula with the other formula as the not connectives sub formula (e.g. if we have a^b as one formula the other must be ~(a^b)).
- a bottom line will then be added to your proof.
To use it backwards:
- select a goal line containing a formula which is just the bottom character and click on NotElimination (or Bottom Introduction as it is the same rule).
- then select a formula which is in the scope of the goal line.
- the converse of the formula selected will then be added as a new goal in your proof.
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