Logiweb aspects of prop three five e two in pyk

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The predefined "pyk" aspect

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

The user defined "the proof aspect" aspect

define proof of prop three five e 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 not metavar var b end metavar equal zero imply metavar var a end metavar times metavar var b end metavar equal zero imply metavar var a end metavar equal zero infer all metavar var a end metavar indeed all metavar var b end metavar indeed not metavar var b end metavar suc equal zero 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 suc equal zero 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 conclude metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar equal zero cut prop three five d conclude metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar equal zero imply not metavar var a end metavar times metavar var b end metavar equal zero 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 imply not metavar var a end metavar times metavar var b end metavar equal zero 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 conclude not metavar var a end metavar times metavar var b end metavar equal zero imply not metavar var a end metavar equal zero cut 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 conclude metavar var a end metavar equal zero 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 suc equal zero infer metavar var a end metavar equal zero conclude metavar var a end metavar times metavar var b end metavar suc equal zero imply metavar var a end metavar equal zero cut deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed not metavar var b end metavar suc equal zero infer metavar var a end metavar times metavar var b end metavar suc equal zero imply metavar var a end metavar equal zero conclude not metavar var b end metavar suc equal zero imply metavar var a end metavar times metavar var b end metavar suc equal zero imply metavar var a end metavar equal zero cut deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed not metavar var b end metavar equal zero imply metavar var a end metavar times metavar var b end metavar equal zero imply metavar var a end metavar equal zero infer not metavar var b end metavar suc equal zero imply metavar var a end metavar times metavar var b end metavar suc equal zero imply metavar var a end metavar equal zero conclude not metavar var b end metavar equal zero imply metavar var a end metavar times metavar var b end metavar equal zero imply metavar var a end metavar equal zero imply not metavar var b end metavar suc equal zero imply metavar var a end metavar times metavar var b end metavar suc equal zero imply metavar var a end metavar equal zero end quote state proof state cache var c end expand end define