Logiweb aspects of prop three five g two in pyk

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The predefined "pyk" aspect

define pyk of prop three five g two 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 w unicode small o unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of prop three five g two 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 four 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 two 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 imply metavar var a end metavar times metavar var b end metavar suc 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 two 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 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 metavar var a end metavar times metavar var b end metavar suc equal zero suc infer axiom s eight conclude metavar var a end metavar times metavar var b end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar cut axiom s one modus ponens metavar var a end metavar times metavar var b end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar modus ponens metavar var a end metavar times metavar var b end metavar suc equal zero suc conclude metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar equal zero suc cut prop three five f conclude metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar equal zero suc imply not 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 times metavar var b end metavar equal zero suc imply not metavar var a end metavar equal zero cut rule mp modus ponens metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar equal zero suc imply not 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 times metavar var b end metavar equal zero suc imply not metavar var a end metavar equal zero modus ponens metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar equal zero suc conclude not 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 times metavar var b end metavar equal zero suc imply not metavar var a end metavar equal zero cut prop three five g three 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 cut prop three five g four 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 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 cut h eleven modus ponens not 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 times metavar var b end metavar equal zero suc imply not metavar var a end metavar equal zero 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 imply not metavar var a end metavar equal zero suc imply not metavar var b end metavar suc equal zero suc 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 imply 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 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 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 metavar var a end metavar times metavar var b end metavar suc 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 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 imply metavar var a end metavar times metavar var b end metavar suc 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