Logiweb aspects of prop three four a two in pyk

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The predefined "pyk" aspect

define pyk of prop three four a 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 o unicode small u unicode small r unicode space unicode small a 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 four a 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 four unicode small a 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 four a two as system s infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar imply metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar suc end define

The user defined "the proof aspect" aspect

define proof of prop three four a 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 c end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar infer axiom s six conclude metavar var b end metavar plus metavar var c end metavar suc equal metavar var b end metavar plus metavar var c end metavar suc cut prop three two o modus ponens metavar var b end metavar plus metavar var c end metavar suc equal metavar var b end metavar plus metavar var c end metavar suc conclude metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc cut axiom s eight conclude metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar plus metavar var a end metavar cut prop three two e modus ponens metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar conclude metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar plus metavar var a end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar cut prop three two j conclude metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar cut prop three two c modus ponens metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar plus metavar var a end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar modus ponens metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar conclude metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar plus metavar var a end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar cut axiom s eight conclude metavar var a end metavar times metavar var c end metavar suc equal metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar cut prop three two i modus ponens metavar var a end metavar times metavar var c end metavar suc equal metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar conclude metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar cut prop three two d modus ponens metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar plus metavar var a end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar modus ponens metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar plus metavar var a end metavar conclude metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar plus metavar var a end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar suc cut prop three two c modus ponens metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar plus metavar var a end metavar modus ponens metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar plus metavar var a end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar suc conclude metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar suc cut prop three two c modus ponens metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc modus ponens metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar suc conclude metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar suc cut deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar infer metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar suc conclude metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar imply metavar var a end metavar times metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar times metavar var b end metavar plus metavar var a end metavar times metavar var c end metavar suc end quote state proof state cache var c end expand end define