Logiweb aspects of prop three five g three in pyk

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The predefined "pyk" aspect

define pyk of prop three five g three as text unicode start of text unicode small p unicode small r unicode small o unicode small p unicode space unicode small t unicode small h unicode small r unicode small e unicode small e unicode space unicode small f unicode small i unicode small v unicode small e unicode space unicode small g unicode space unicode small t unicode small h unicode small r unicode small e unicode small e unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of prop three five g three as text unicode start of text unicode newline unicode capital p unicode small r unicode small o unicode small p unicode backslash unicode space unicode three unicode period unicode five unicode small g unicode underscore unicode two unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of prop three five g three as system s infer all metavar var a end metavar indeed all metavar var b end metavar indeed not metavar var a end metavar times metavar var b end metavar equal zero imply not metavar var a end metavar equal zero suc imply not metavar var a end metavar equal zero suc imply not metavar var b end metavar suc equal zero suc end define

The user defined "the proof aspect" aspect

define proof of prop three five g three as lambda var c dot lambda var x dot proof expand quote system s infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed not metavar var a end metavar times metavar var b end metavar equal zero imply not metavar var a end metavar equal zero suc infer conjel2 modus ponens not metavar var a end metavar times metavar var b end metavar equal zero imply not metavar var a end metavar equal zero suc conclude metavar var a end metavar equal zero suc cut conjel1 modus ponens not metavar var a end metavar times metavar var b end metavar equal zero imply not metavar var a end metavar equal zero suc conclude metavar var a end metavar times metavar var b end metavar equal zero cut axiom s three conclude not zero equal zero suc cut h ten modus ponens not zero equal zero suc conclude not zero suc equal zero cut h four mark conclude metavar var a end metavar equal zero suc imply metavar var a end metavar equal zero imply zero suc equal zero cut h three modus ponens metavar var a end metavar equal zero suc imply metavar var a end metavar equal zero imply zero suc equal zero modus ponens metavar var a end metavar equal zero suc modus ponens not zero suc equal zero conclude not metavar var a end metavar equal zero cut prop three two n conclude metavar var a end metavar times metavar var b end metavar equal metavar var b end metavar times metavar var a end metavar cut axiom s one modus ponens metavar var a end metavar times metavar var b end metavar equal metavar var b end metavar times metavar var a end metavar modus ponens metavar var a end metavar times metavar var b end metavar equal zero conclude metavar var b end metavar times metavar var a end metavar equal zero cut prop three five e conclude not metavar var a end metavar equal zero imply metavar var b end metavar times metavar var a end metavar equal zero imply metavar var b end metavar equal zero cut rule mp modus ponens not metavar var a end metavar equal zero imply metavar var b end metavar times metavar var a end metavar equal zero imply metavar var b end metavar equal zero modus ponens not metavar var a end metavar equal zero conclude metavar var b end metavar times metavar var a end metavar equal zero imply metavar var b end metavar equal zero cut rule mp modus ponens metavar var b end metavar times metavar var a end metavar equal zero imply metavar var b end metavar equal zero modus ponens metavar var b end metavar times metavar var a end metavar equal zero conclude metavar var b end metavar equal zero cut axiom s two modus ponens metavar var b end metavar equal zero conclude metavar var b end metavar suc equal zero suc cut conjin modus ponens metavar var a end metavar equal zero suc modus ponens metavar var b end metavar suc equal zero suc conclude not metavar var a end metavar equal zero suc imply not metavar var b end metavar suc equal zero suc cut deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed not metavar var a end metavar times metavar var b end metavar equal zero imply not metavar var a end metavar equal zero suc infer not metavar var a end metavar equal zero suc imply not metavar var b end metavar suc equal zero suc conclude not metavar var a end metavar times metavar var b end metavar equal zero imply not metavar var a end metavar equal zero suc imply not metavar var a end metavar equal zero suc imply not metavar var b end metavar suc equal zero suc end quote state proof state cache var c end expand end define