Logiweb aspects of lemma plusF(Sym) in pyk

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The predefined "pyk" aspect

define pyk of lemma plusF(Sym) 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 l unicode small u unicode small s unicode capital f unicode left parenthesis unicode capital s unicode small y unicode small m unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma plusF(Sym) as text unicode start of text unicode capital p unicode small l unicode small u unicode small s unicode capital f unicode left parenthesis unicode capital s unicode small y unicode small m 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 plusF(Sym) as system Q infer all metavar var m end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] = [ 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 metavar var m end metavar indeed not0 placeholder-var var d end var = 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 fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end define

The user defined "the proof aspect" aspect

define proof of lemma plusF(Sym) 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 fx end metavar indeed all metavar var fy end metavar indeed axiom plusF conclude [ 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 metavar var m end metavar indeed not0 placeholder-var var d end var = 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 fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] cut lemma eqSymmetry modus ponens [ 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 metavar var m end metavar indeed not0 placeholder-var var d end var = 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 fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] conclude [ metavar var fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] = [ 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 metavar var m end metavar indeed not0 placeholder-var var d end var = 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 fx end metavar ; metavar var m end metavar ] + [ metavar var fy end metavar ; metavar var m end metavar ] end pair end pair end set ; metavar var m end metavar ] end quote state proof state cache var c end expand end define