Fwd: Add fixity for (==) and (/=)

---------- Forwarded message --------- From: Dannyu NDos Date: 2018년 9월 17일 (월) 오후 6:18 Subject: Re: Add fixity for (==) and (/=) To: Proof by truth table (F is False, T is True): p q r (p == q) (q == r) ((p == q) == r) (p == (q == r)) F F F T T F F F F T T F T T F T F F F T T F T T F T F F T F F F T T T T F T F F F F T T F T F F F T T T T T T T That proves associativity of (==). Also note that p /= q ≡ not p == q. Proof: p q (p /= q) (not p) (not p == q) F F F T F F T T T T T F T F T T T F F F And by symmetry of (/=), p /= q ≡ p == not q. Then: (p /= q) /= r ≡ (not p == q) == not r ≡ not p == (q == not r) ≡ p /= (q /= r). Hence (/=) is associative. Q.E.D.