define pyk of prop three four c one 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 c unicode space unicode small o unicode small n unicode small e unicode end of text end unicode text end text end define
define tex of prop three four c one 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 c unicode underscore unicode one unicode end of text end unicode text end text end define
define statement of prop three four c one 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 times zero equal metavar var a end metavar times metavar var b end metavar times zero end define
define proof of prop three four c one 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 axiom s seven conclude metavar var a end metavar times metavar var b end metavar times zero equal zero cut axiom s seven conclude metavar var b end metavar times zero equal zero cut prop three two o modus ponens metavar var b end metavar times zero equal zero conclude metavar var a end metavar times metavar var b end metavar times zero equal metavar var a end metavar times zero cut axiom s seven conclude metavar var a end metavar times zero equal zero cut prop three two c modus ponens metavar var a end metavar times metavar var b end metavar times zero equal metavar var a end metavar times zero modus ponens metavar var a end metavar times zero equal zero conclude metavar var a end metavar times metavar var b end metavar times zero equal zero cut prop three two d modus ponens metavar var a end metavar times metavar var b end metavar times zero equal zero modus ponens metavar var a end metavar times metavar var b end metavar times zero equal zero conclude metavar var a end metavar times metavar var b end metavar times zero equal metavar var a end metavar times metavar var b end metavar times zero end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,