Emoji
Wed, 21 Sep 2016 13:04:12 GMT

§4 - GÖDEL COMPLETENESS THEOREM - The next rule will allow us to bring every formula involving quantifiers into a form in which it begins with a quantifier. Let A SMILEY WITH SQUINTED EYES) have x as the only free variable and let every occurrence of x be free. Let B be a statement which does not contain x. Then the following are valid statements. (\lnot(\forall x A SMILEY WITH SQUINTED EYES))) \leftrightarrow (\exists x\lnot(A SMILEY WITH SQUINTED EYES))), ((\forall x A SMILEY WITH SQUINTED EYES)) & SMILING FROG FACE)) \leftrightarrow (\forall x((A SMILEY WITH SQUINTED EYES)) & SMILING FROG FACE))), ((\exists x A SMILEY WITH SQUINTED EYES)) & SMILING FROG FACE)) \leftrightarrow (\exists x ((A SMILEY WITH SQUINTED EYES)) & SMILING FROG FACE)).