Commit 8355c341737a2bd35d4ab8c2ec952f9345da2d20 - Maxixe

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). Raw diff Collapse all Expand all

+35

-0

doc/Examples.md less more

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