Logiweb aspects of lemma exp(+1) in pyk

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The predefined "pyk" aspect

define pyk of lemma exp(+1) 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 e unicode small x unicode small p unicode left parenthesis unicode plus sign unicode one unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma exp(+1) as text unicode start of text unicode capital e unicode small x unicode small p unicode left parenthesis unicode plus sign unicode one 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 exp(+1) as system Q infer all metavar var m end metavar indeed all metavar var x end metavar indeed 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 end define

The user defined "the proof aspect" aspect

define proof of lemma exp(+1) 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 lemma +1IsPositive(N) conclude not0 0 <= metavar var m end metavar + 1 imply not0 not0 0 = metavar var m end metavar + 1 cut 1rule expPositive modus ponens not0 0 <= metavar var m end metavar + 1 imply not0 not0 0 = metavar var m end metavar + 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 + 1 + - 1 cut lemma x=x+y-y conclude metavar var m end metavar = metavar var m end metavar + 1 + - 1 cut lemma sameExp modus ponens metavar var m end metavar = metavar var m end metavar + 1 + - 1 conclude metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var m end metavar + 1 + - 1 cut lemma eqMultiplicationLeft modus ponens metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar ^ metavar var m end metavar + 1 + - 1 conclude metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar + 1 + - 1 cut lemma eqSymmetry modus ponens metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar = metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar + 1 + - 1 conclude metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar + 1 + - 1 = metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar cut lemma eqTransitivity 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 + 1 + - 1 modus ponens metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar + 1 + - 1 = metavar var x end metavar * metavar var x end metavar ^ metavar var m end metavar 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 end quote state proof state cache var c end expand end define