Logiweb aspects of lemma crsIsTotal in pyk

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The predefined "pyk" aspect

define pyk of lemma crsIsTotal 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 r unicode small s unicode capital i unicode small s unicode capital t unicode small o unicode small t unicode small a unicode small l unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma crsIsTotal as text unicode start of text unicode capital c unicode small r unicode small s unicode capital i unicode small s unicode capital t unicode small o unicode small t unicode small a unicode small l unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma crsIsTotal as system Q infer all metavar var m end metavar indeed all metavar var x end metavar indeed lambda var c dot typeRational0( quote metavar var x end metavar end quote ) endorse metavar var m end metavar in0 N infer zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma metavar var x end metavar end pair end pair in0 the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma metavar var x end metavar end pair end pair end set end define

The user defined "the proof aspect" aspect

define proof of lemma crsIsTotal 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 lambda var c dot typeRational0( quote metavar var x end metavar end quote ) endorse metavar var m end metavar in0 N infer axiom rationalType modus probans lambda var c dot typeRational0( quote metavar var x end metavar end quote ) conclude metavar var x end metavar in0 Q cut lemma toCartProd modus ponens metavar var m end metavar in0 N modus ponens metavar var x end metavar in0 Q conclude zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma metavar var x end metavar end pair end pair in0 the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set cut lemma eqReflexivity conclude zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma metavar var x end metavar end pair end pair = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma metavar var x end metavar end pair end pair cut pred lemma intro exist at metavar var m end metavar modus ponens zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma metavar var x end metavar end pair end pair = zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma metavar var x end metavar end pair end pair conclude not0 for all objects object var var crs1 end var indeed not0 zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma metavar var x end metavar end pair end pair = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma metavar var x end metavar end pair end pair cut lemma formula2separation modus ponens zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma metavar var x end metavar end pair end pair in0 the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set modus ponens not0 for all objects object var var crs1 end var indeed not0 zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma metavar var x end metavar end pair end pair = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma metavar var x end metavar end pair end pair conclude zermelo pair zermelo pair metavar var m end metavar comma metavar var m end metavar end pair comma zermelo pair metavar var m end metavar comma metavar var x end metavar end pair end pair in0 the set of ph in the set of ph in power power U( zermelo pair N comma Q end pair ) end power end power such that not0 for all objects object var var op1 end var indeed not0 not0 for all objects object var var op2 end var indeed not0 not0 not0 object var var op1 end var in0 N imply not0 object var var op2 end var in0 Q imply not0 placeholder-var var a end var = zermelo pair zermelo pair object var var op1 end var comma object var var op1 end var end pair comma zermelo pair object var var op1 end var comma object var var op2 end var end pair end pair end set such that not0 for all objects object var var crs1 end var indeed not0 placeholder-var var c end var = zermelo pair zermelo pair object var var crs1 end var comma object var var crs1 end var end pair comma zermelo pair object var var crs1 end var comma metavar var x end metavar end pair end pair end set end quote state proof state cache var c end expand end define