git @ Cat's Eye Technologies
Attempt a proof by contradiction. It doesn't quite work. Chris Pressey 4 years ago
1 changed file(s) with 35 addition(s) and 0 deletion(s).
 112 112 end 113 113 end 114 114 Step_6 = or(b, a) by Tautology with Step_5 115 qed 116 ===> ok 117 118 ### Proof by Contradiction ### 119 120 If we assume p and show that it leads to a contradiction, 121 we can then infer ¬p. If we can use proof by contradiction, 122 we can derive Modus Tollens. 123 124 given 125 Modus_Ponens = impl(P, Q) ; P |- Q 126 127 Double_Negation = not(not(P)) |- P 128 Contradiction = P ; not(P) |- bottom 129 Explosion = bottom |- P 130 131 block Reductio_ad_Absurdum 132 Supposition = A{term} |- A 133 Conclusion = bottom |- not(A) 134 end 135 136 Premise_1 = |- impl(p, q) 137 Premise_2 = |- not(q) 138 show 139 not(p) 140 proof 141 Step_1 = impl(p, q) by Premise_1 142 Step_2 = not(q) by Premise_2 143 block Reductio_ad_Absurdum 144 Step_3 = p by Supposition with p 145 Step_4 = q by Modus_Ponens with Step_1, Step_3 146 Step_5 = bottom by Contradiction with Step_4, Step_2 147 Step_6 = not(p) by Conclusion with Step_5 148 end 149 Step_7 = not(p) by Tautology with Step_6 115 150 qed 116 151 ===> ok 117 152