Logiweb aspects of lemma positiveBase indu in pyk

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The predefined "pyk" aspect

define pyk of lemma positiveBase indu 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 b unicode small a unicode small s unicode small e unicode space unicode small i unicode small n unicode small d unicode small u unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma positiveBase indu 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 b unicode small a unicode small s unicode small e unicode left parenthesis unicode capital i unicode small n unicode small d unicode small u unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma positiveBase indu as system Q infer all metavar var m end metavar indeed 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 <= metavar var x end metavar ^ metavar var m end metavar imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar imply not0 0 <= metavar var x end metavar ^ metavar var m end metavar + 1 imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar + 1 end define

The user defined "the proof aspect" aspect

define proof of lemma positiveBase indu as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var m end metavar indeed 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 <= metavar var x end metavar ^ metavar var m end metavar imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar infer lemma exp(+1) conclude metavar var x end metavar ^ metavar var m end metavar + 1 = metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar ^ metavar var m end metavar + 1 = metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar conclude metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var m end metavar + 1 cut lemma positiveFactors modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar modus ponens not0 0 <= metavar var x end metavar ^ metavar var m end metavar imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar conclude not0 0 <= metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar imply not0 not0 0 = metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar cut lemma subLessRight modus ponens metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var m end metavar + 1 modus ponens not0 0 <= metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar imply not0 not0 0 = metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar conclude not0 0 <= metavar var x end metavar ^ metavar var m end metavar + 1 imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar + 1 cut all metavar var m end metavar indeed all metavar var x end metavar indeed 1rule deduction modus ponens all metavar var m end metavar indeed 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 <= metavar var x end metavar ^ metavar var m end metavar imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar infer not0 0 <= metavar var x end metavar ^ metavar var m end metavar + 1 imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar + 1 conclude not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar imply not0 0 <= metavar var x end metavar ^ metavar var m end metavar imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar imply not0 0 <= metavar var x end metavar ^ metavar var m end metavar + 1 imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar + 1 cut not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar infer 1rule mp modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar imply not0 0 <= metavar var x end metavar ^ metavar var m end metavar imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar imply not0 0 <= metavar var x end metavar ^ metavar var m end metavar + 1 imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar + 1 modus ponens not0 0 <= metavar var x end metavar imply not0 not0 0 = metavar var x end metavar conclude not0 0 <= metavar var x end metavar ^ metavar var m end metavar imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar imply not0 0 <= metavar var x end metavar ^ metavar var m end metavar + 1 imply not0 not0 0 = metavar var x end metavar ^ metavar var m end metavar + 1 end quote state proof state cache var c end expand end define