Logiweb aspects of lemma x<=|x| in pyk

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The predefined "pyk" aspect

define pyk of lemma x<=|x| 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 x unicode less than unicode equal sign unicode vertical line unicode small x unicode vertical line unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma x<=|x| as text unicode start of text unicode small x unicode less than unicode equal sign unicode vertical line unicode small x unicode vertical line unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma x<=|x| as system Q infer all metavar var x end metavar indeed metavar var x end metavar <= | metavar var x end metavar | end define

The user defined "the proof aspect" aspect

define proof of lemma x<=|x| as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed 0 <= metavar var x end metavar infer lemma nonnegativeNumerical conclude | metavar var x end metavar | = metavar var x end metavar cut lemma eqSymmetry modus ponens | metavar var x end metavar | = metavar var x end metavar conclude metavar var x end metavar = | metavar var x end metavar | cut lemma eqLeq modus ponens metavar var x end metavar = | metavar var x end metavar | conclude metavar var x end metavar <= | metavar var x end metavar | cut all metavar var x end metavar indeed metavar var x end metavar <= 0 infer lemma 0<=|x| conclude 0 <= | metavar var x end metavar | cut lemma leqTransitivity modus ponens metavar var x end metavar <= 0 modus ponens 0 <= | metavar var x end metavar | conclude metavar var x end metavar <= | metavar var x end metavar | cut all metavar var x end metavar indeed 1rule deduction modus ponens all metavar var x end metavar indeed 0 <= metavar var x end metavar infer metavar var x end metavar <= | metavar var x end metavar | conclude 0 <= metavar var x end metavar imply metavar var x end metavar <= | metavar var x end metavar | cut 1rule deduction modus ponens all metavar var x end metavar indeed metavar var x end metavar <= 0 infer metavar var x end metavar <= | metavar var x end metavar | conclude metavar var x end metavar <= 0 imply metavar var x end metavar <= | metavar var x end metavar | cut lemma from leqGeq modus ponens 0 <= metavar var x end metavar imply metavar var x end metavar <= | metavar var x end metavar | modus ponens metavar var x end metavar <= 0 imply metavar var x end metavar <= | metavar var x end metavar | conclude metavar var x end metavar <= | metavar var x end metavar | end quote state proof state cache var c end expand end define