The following box-proof uses only the implication rules (e.g. no classical contradiction). 1: assumption 2: assumption 3: assumption 4: assumption 5: 6: 7: 8: 9: 10: 11: 12: (((A-B)-A)-A)-B)-B intro...

Extracted text: The following box-proof uses only the implication rules (e.g. no classical contradiction). 1: assumption 2: assumption 3: assumption 4: assumption 5: 6: 7: 8: 9: 10: 11: 12: (((A-B)-A)-A)-B)-B intro 1-11 Select one or more: The box-proof contains 4 boxes. - line 5 and line 11 contains the same propositional formula line 8 is justified by an application of the -elim rule The box proof contains 5 boxes and one of the hidden annotations is an assumption. line 8 is justified by an application of the -intro rule * line 6 and line 10 contains the same propositional formula * line 6: ((A B) A)- A - line 4: (A B) A