Logiweb aspects of lemma closetolessIsLess in pyk

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The predefined "pyk" aspect

define pyk of lemma closetolessIsLess 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 l unicode small e unicode small s unicode small s unicode capital i unicode small s unicode capital l unicode small e unicode small s unicode small s unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma closetolessIsLess 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 l unicode small e unicode small s unicode small s unicode capital i unicode small s unicode capital l unicode small e unicode small s unicode small s unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma closetolessIsLess as system Q infer all metavar var x1 end metavar indeed all metavar var x2 end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x1 end metavar <= metavar var y end metavar + - metavar var z end metavar infer not0 | metavar var x1 end metavar + - metavar var x2 end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var x1 end metavar + - metavar var x2 end metavar | = 1/ 1 + 1 + 1 * metavar var z end metavar infer metavar var x2 end metavar <= metavar var y end metavar + - 1/ 1 + 1 + 1 * metavar var z end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma closetolessIsLess as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x1 end metavar indeed all metavar var x2 end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x1 end metavar <= metavar var y end metavar + - metavar var z end metavar infer not0 | metavar var x1 end metavar + - metavar var x2 end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var x1 end metavar + - metavar var x2 end metavar | = 1/ 1 + 1 + 1 * metavar var z end metavar infer lemma 0<=|x| conclude 0 <= | metavar var x1 end metavar + - metavar var x2 end metavar | cut lemma leqLessTransitivity modus ponens 0 <= | metavar var x1 end metavar + - metavar var x2 end metavar | modus ponens not0 | metavar var x1 end metavar + - metavar var x2 end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var x1 end metavar + - metavar var x2 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 y end metavar + - metavar var y end metavar | = 0 cut lemma eqSymmetry modus ponens | metavar var y end metavar + - metavar var y end metavar | = 0 conclude 0 = | metavar var y end metavar + - metavar var y end metavar | cut lemma subLessLeft modus ponens 0 = | metavar var y end metavar + - metavar var y 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 y end metavar + - metavar var y end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var y end metavar + - metavar var y end metavar | = 1/ 1 + 1 + 1 * metavar var z end metavar cut lemma preserveLessGreater modus ponens metavar var x1 end metavar <= metavar var y end metavar + - metavar var z end metavar modus ponens not0 | metavar var x1 end metavar + - metavar var x2 end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var x1 end metavar + - metavar var x2 end metavar | = 1/ 1 + 1 + 1 * metavar var z end metavar modus ponens not0 | metavar var y end metavar + - metavar var y end metavar | <= 1/ 1 + 1 + 1 * metavar var z end metavar imply not0 not0 | metavar var y end metavar + - metavar var y end metavar | = 1/ 1 + 1 + 1 * metavar var z end metavar conclude metavar var x2 end metavar <= metavar var y end metavar + - 1/ 1 + 1 + 1 * metavar var z end metavar end quote state proof state cache var c end expand end define