define pyk of prop three two o 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 o unicode end of text end unicode text end text end define
define tex of prop three two o 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 o unicode end of text end unicode text end text end define
define statement of prop three two o 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 equal metavar var b end metavar infer metavar var c end metavar times metavar var a end metavar equal metavar var c end metavar times metavar var b end metavar end define
define proof of prop three two o 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 equal metavar var b end metavar infer prop three two k conclude metavar var a end metavar equal metavar var b end metavar imply metavar var a end metavar times metavar var c end metavar equal metavar var b end metavar times metavar var c end metavar cut metavar var a end metavar equal metavar var b end metavar imply metavar var a end metavar times metavar var c end metavar equal metavar var b end metavar times metavar var c end metavar modus ponens metavar var a end metavar equal metavar var b end metavar conclude metavar var a end metavar times metavar var c end metavar equal metavar var b end metavar times metavar var c end metavar cut prop three two n conclude metavar var a end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var a end metavar cut prop three two n conclude metavar var b end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var b end metavar cut prop three two c conclude metavar var a end metavar times metavar var c end metavar equal metavar var b end metavar times metavar var c end metavar imply metavar var b end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var b end metavar imply metavar var a end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var b end metavar cut metavar var a end metavar times metavar var c end metavar equal metavar var b end metavar times metavar var c end metavar imply metavar var b end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var b end metavar imply metavar var a end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var b end metavar modus ponens metavar var a end metavar times metavar var c end metavar equal metavar var b end metavar times metavar var c end metavar modus ponens metavar var b end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var b end metavar conclude metavar var a end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var b end metavar cut axiom s one conclude metavar var a end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var b end metavar imply metavar var a end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var a end metavar imply metavar var c end metavar times metavar var a end metavar equal metavar var c end metavar times metavar var b end metavar cut metavar var a end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var b end metavar imply metavar var a end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var a end metavar imply metavar var c end metavar times metavar var a end metavar equal metavar var c end metavar times metavar var b end metavar modus ponens metavar var a end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var b end metavar modus ponens metavar var a end metavar times metavar var c end metavar equal metavar var c end metavar times metavar var a end metavar conclude metavar var c end metavar times metavar var a end metavar equal metavar var c end metavar times metavar var b end metavar 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 equal metavar var b end metavar infer metavar var c end metavar times metavar var a end metavar equal metavar var c end metavar times metavar var b end metavar conclude metavar var a end metavar equal metavar var b end metavar imply metavar var c end metavar times metavar var a end metavar equal metavar var c end metavar times 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,