Logiweb aspects of prop three five f two in pyk

Up Help

The predefined "pyk" aspect

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

The user defined "the proof aspect" aspect

define proof of prop three five f 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 plus metavar var b end metavar equal zero suc imply not not metavar var a end metavar equal zero imply not 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 infer all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar plus metavar var b end metavar suc equal zero suc infer axiom s six conclude metavar var a end metavar plus metavar var b end metavar suc equal metavar var a end metavar plus metavar var b end metavar suc cut axiom s one modus ponens metavar var a end metavar plus metavar var b end metavar suc equal metavar var a end metavar plus metavar var b end metavar suc modus ponens metavar var a end metavar plus metavar var b end metavar suc equal zero suc conclude metavar var a end metavar plus metavar var b end metavar suc equal zero suc cut axiom s four modus ponens metavar var a end metavar plus metavar var b end metavar suc equal zero suc conclude metavar var a end metavar plus metavar var b end metavar equal zero cut prop three five d conclude metavar var a end metavar plus metavar var b end metavar equal zero imply not metavar var a end metavar equal zero imply not metavar var b end metavar equal zero cut rule mp modus ponens metavar var a end metavar plus metavar var b end metavar equal zero imply not metavar var a end metavar equal zero imply not metavar var b end metavar equal zero modus ponens metavar var a end metavar plus metavar var b end metavar equal zero conclude not metavar var a end metavar equal zero imply not metavar var b end metavar equal zero cut conjel1 modus ponens not metavar var a end metavar equal zero imply not metavar var b end metavar equal zero conclude metavar var a end metavar equal zero cut conjel2 modus ponens not metavar var a end metavar equal zero imply not metavar var b 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 modus ponens metavar var b end metavar suc equal zero suc conclude not metavar var a end metavar equal zero imply not metavar var b end metavar suc equal zero suc cut disjin1 modus ponens not metavar var a end metavar equal zero imply not metavar var b end metavar suc equal zero suc conclude not not metavar var a end metavar equal zero imply not 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 cut deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar plus metavar var b end metavar suc equal zero suc infer not not metavar var a end metavar equal zero imply not 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 conclude metavar var a end metavar plus metavar var b end metavar suc equal zero suc imply not not metavar var a end metavar equal zero imply not 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 cut deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar plus metavar var b end metavar equal zero suc imply not not metavar var a end metavar equal zero imply not 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 infer metavar var a end metavar plus metavar var b end metavar suc equal zero suc imply not not metavar var a end metavar equal zero imply not 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 conclude metavar var a end metavar plus metavar var b end metavar equal zero suc imply not not metavar var a end metavar equal zero imply not 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 imply metavar var a end metavar plus metavar var b end metavar suc equal zero suc imply not not metavar var a end metavar equal zero imply not 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 end quote state proof state cache var c end expand end define