Logiweb aspects of prop three five g four in pyk

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The predefined "pyk" aspect

define pyk of prop three five g four 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 f unicode small o unicode small u unicode small r unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of prop three five g four 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 three 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 four as system s infer all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar times metavar var b end metavar equal zero suc imply not metavar var a end metavar equal zero suc imply not metavar var b end metavar equal zero suc infer not metavar var a end metavar times metavar var b end metavar equal zero suc imply not metavar var a end metavar equal zero 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 four 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 metavar var a end metavar times metavar var b end metavar equal zero suc imply not metavar var a end metavar equal zero suc imply not metavar var b end metavar equal zero suc 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 suc imply not metavar var a end metavar equal zero infer conjel1 modus ponens not metavar var a end metavar times metavar var b end metavar equal zero suc imply not metavar var a end metavar equal zero conclude metavar var a end metavar times metavar var b end metavar equal zero suc cut rule mp modus ponens metavar var a end metavar times metavar var b end metavar equal zero suc imply not metavar var a end metavar equal zero suc imply not metavar var b end metavar equal zero suc modus ponens metavar var a end metavar times metavar var b end metavar equal zero suc conclude not metavar var a end metavar equal zero suc imply not metavar var b end metavar equal zero suc cut conjel1 modus ponens not metavar var a end metavar equal zero suc imply not metavar var b end metavar equal zero suc conclude metavar var a end metavar equal zero suc cut conjel2 modus ponens not metavar var a end metavar times metavar var b end metavar equal zero suc imply not metavar var a end metavar equal zero conclude metavar var a end metavar equal zero cut axiom s one modus ponens metavar var a end metavar equal zero modus ponens metavar var a end metavar equal zero suc conclude zero equal zero suc cut axiom s three conclude not zero equal zero suc cut t one conclude not zero equal zero suc imply zero equal zero suc imply not metavar var a end metavar equal zero suc imply not metavar var b end metavar suc equal zero suc cut rule mp modus ponens not zero equal zero suc imply zero equal zero suc imply not metavar var a end metavar equal zero suc imply not metavar var b end metavar suc equal zero suc modus ponens not zero equal zero suc conclude zero equal zero suc imply not metavar var a end metavar equal zero suc imply not metavar var b end metavar suc equal zero suc cut rule mp modus ponens zero equal zero suc imply not metavar var a end metavar equal zero suc imply not metavar var b end metavar suc equal zero suc modus ponens zero 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 suc imply not metavar var a end metavar equal zero 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 suc imply not metavar var a end metavar equal zero 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