define pyk of prop three two k 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 t unicode small w unicode small o unicode space unicode small k 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 two k 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 two unicode small k unicode underscore unicode one unicode end of text end unicode text end text end define
define statement of prop three two k one as system s infer for all terms metavar var a end metavar comma metavar var b end metavar indeed metavar var a end metavar equal metavar var b end metavar infer metavar var a end metavar times zero equal metavar var b end metavar times zero end define
define proof of prop three two k one as lambda var c dot lambda var x dot proof expand quote system s infer any term metavar var a end metavar comma metavar var b end metavar end line axiom s seven conclude metavar var a end metavar times zero equal zero cut axiom s seven conclude metavar var b end metavar times zero equal zero cut prop three two a conclude zero equal zero cut prop three two b modus ponens metavar var b end metavar times zero equal zero conclude zero equal metavar var b end metavar times zero cut prop three two c conclude metavar var a end metavar times zero equal zero imply zero equal metavar var b end metavar times zero imply metavar var a end metavar times zero equal metavar var b end metavar times zero cut metavar var a end metavar times zero equal zero imply zero equal metavar var b end metavar times zero imply metavar var a end metavar times zero equal metavar var b end metavar times zero modus ponens metavar var a end metavar times zero equal zero modus ponens zero equal metavar var b end metavar times zero conclude metavar var a end metavar times zero equal 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,