define pyk of prop three four d 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 d 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 d 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 d unicode underscore unicode one unicode end of text end unicode text end text end define
define statement of prop three four d one as system s infer all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar plus zero equal metavar var b end metavar plus zero imply metavar var a end metavar equal metavar var b end metavar end define
define proof of prop three four d 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 all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar plus zero equal metavar var b end metavar plus zero infer axiom s five conclude metavar var a end metavar plus zero equal metavar var a end metavar cut axiom s five conclude metavar var b end metavar plus zero equal metavar var b end metavar cut axiom s one modus ponens metavar var a end metavar plus zero equal metavar var a end metavar modus ponens metavar var a end metavar plus zero equal metavar var b end metavar plus zero conclude metavar var a end metavar equal metavar var b end metavar plus zero cut prop three two c modus ponens metavar var a end metavar equal metavar var b end metavar plus zero modus ponens metavar var b end metavar plus zero equal metavar var b end metavar conclude metavar var a end metavar equal metavar var b end metavar cut deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar plus zero equal metavar var b end metavar plus zero infer metavar var a end metavar equal metavar var b end metavar conclude metavar var a end metavar plus zero equal metavar var b end metavar plus zero imply metavar var a end metavar equal metavar var b end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,