Logiweb aspects of lemma closetogreaterIsGreater in pyk

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The predefined "pyk" aspect

define pyk of lemma closetogreaterIsGreater as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small c unicode small l unicode small o unicode small s unicode small e unicode small t unicode small o unicode small g unicode small r unicode small e unicode small a unicode small t unicode small e unicode small r unicode capital i unicode small s unicode capital g unicode small r unicode small e unicode small a unicode small t unicode small e unicode small r unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma closetogreaterIsGreater as text unicode start of text unicode capital c unicode small l unicode small o unicode small s unicode small e unicode small t unicode small o unicode small g unicode small r unicode small e unicode small a unicode small t unicode small e unicode small r unicode capital i unicode small s unicode capital g unicode small r unicode small e unicode small a unicode small t unicode small e unicode small r unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma closetogreaterIsGreater as system Q infer all metavar var x end metavar indeed all metavar var y1 end metavar indeed all metavar var y2 end metavar indeed all metavar var z end metavar indeed metavar var x end metavar <= metavar var y1 end metavar + - metavar var z end metavar infer not0 | metavar var y1 end metavar + - metavar var y2 end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var y1 end metavar + - metavar var y2 end metavar | = 1/ 1 + 1 + 1 * metavar var z end metavar infer metavar var x end metavar <= metavar var y2 end metavar + - 1/ 1 + 1 + 1 * metavar var z end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma closetogreaterIsGreater as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed all metavar var y1 end metavar indeed all metavar var y2 end metavar indeed all metavar var z end metavar indeed metavar var x end metavar <= metavar var y1 end metavar + - metavar var z end metavar infer not0 | metavar var y1 end metavar + - metavar var y2 end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var y1 end metavar + - metavar var y2 end metavar | = 1/ 1 + 1 + 1 * metavar var z end metavar infer lemma 0<=|x| conclude 0 <= | metavar var y1 end metavar + - metavar var y2 end metavar | cut lemma leqLessTransitivity modus ponens 0 <= | metavar var y1 end metavar + - metavar var y2 end metavar | modus ponens not0 | metavar var y1 end metavar + - metavar var y2 end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var y1 end metavar + - metavar var y2 end metavar | = 1/ 1 + 1 + 1 * metavar var z end metavar conclude not0 0 <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 0 = 1/ 1 + 1 + 1 * metavar var z end metavar cut lemma |x-x|=0 conclude | metavar var x end metavar + - metavar var x end metavar | = 0 cut lemma eqSymmetry modus ponens | metavar var x end metavar + - metavar var x end metavar | = 0 conclude 0 = | metavar var x end metavar + - metavar var x end metavar | cut lemma subLessLeft modus ponens 0 = | metavar var x end metavar + - metavar var x end metavar | modus ponens not0 0 <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 0 = 1/ 1 + 1 + 1 * metavar var z end metavar conclude not0 | metavar var x end metavar + - metavar var x end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var x end metavar + - metavar var x end metavar | = 1/ 1 + 1 + 1 * metavar var z end metavar cut lemma preserveLessGreater modus ponens metavar var x end metavar <= metavar var y1 end metavar + - metavar var z end metavar modus ponens not0 | metavar var x end metavar + - metavar var x end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var x end metavar + - metavar var x end metavar | = 1/ 1 + 1 + 1 * metavar var z end metavar modus ponens not0 | metavar var y1 end metavar + - metavar var y2 end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var y1 end metavar + - metavar var y2 end metavar | = 1/ 1 + 1 + 1 * metavar var z end metavar conclude metavar var x end metavar <= metavar var y2 end metavar + - 1/ 1 + 1 + 1 * metavar var z end metavar end quote state proof state cache var c end expand end define