Logiweb aspects of lemma positiveHalved in pyk

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The predefined "pyk" aspect

define pyk of lemma positiveHalved 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 p unicode small o unicode small s unicode small i unicode small t unicode small i unicode small v unicode small e unicode capital h unicode small a unicode small l unicode small v unicode small e unicode small d unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma positiveHalved as text unicode start of text unicode capital p unicode small o unicode small s unicode small i unicode small t unicode small i unicode small v unicode small e unicode capital h unicode small a unicode small l unicode small v unicode small e unicode small d unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma positiveHalved as system Q infer all metavar var x end metavar indeed not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer not0 0 <= 1/ 1 + 1 * metavar var x end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma positiveHalved as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer lemma 0<1/2 conclude not0 0 <= 1/ 1 + 1 imply not0 not0 0 = 1/ 1 + 1 cut lemma lessMultiplicationLeft modus ponens not0 0 <= 1/ 1 + 1 imply not0 not0 0 = 1/ 1 + 1 modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude not0 1/ 1 + 1 * 0 <= 1/ 1 + 1 * metavar var x end metavar imply not0 not0 1/ 1 + 1 * 0 = 1/ 1 + 1 * metavar var x end metavar cut lemma x*0=0 conclude 1/ 1 + 1 * 0 = 0 cut lemma subLessLeft modus ponens 1/ 1 + 1 * 0 = 0 modus ponens not0 1/ 1 + 1 * 0 <= 1/ 1 + 1 * metavar var x end metavar imply not0 not0 1/ 1 + 1 * 0 = 1/ 1 + 1 * metavar var x end metavar conclude not0 0 <= 1/ 1 + 1 * metavar var x end metavar imply not0 not0 0 = 1/ 1 + 1 * metavar var x end metavar end quote state proof state cache var c end expand end define