define pyk of prop three two j 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 t unicode small w unicode small o unicode space unicode small j unicode space unicode small t unicode small w unicode small o unicode end of text end unicode text end text end define
define tex of prop three two j 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 two unicode small j unicode underscore unicode two unicode end of text end unicode text end text end define
define statement of prop three two j two as system s infer for all terms metavar var a end metavar comma metavar var b end metavar comma metavar var c end metavar indeed metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar imply metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc end define
define proof of prop three two j two 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 comma metavar var c end metavar end line block any term macro indent metavar var a end metavar comma metavar var b end metavar comma metavar var c end metavar end line macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar infer axiom s six conclude macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc cut axiom s two modus ponens macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar conclude macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc cut prop three two c modus ponens macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc modus ponens macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc conclude macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc cut axiom s six conclude macro indent 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 i modus ponens macro indent 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 macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc cut axiom s six conclude macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc cut prop three two c modus ponens macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc modus ponens macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc conclude macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc cut because prop three two d modus ponens macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc modus ponens macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc indeed macro indent metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc end line line ell j end block deduction modus ponens ell j conclude metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar imply metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc equal metavar var a end metavar plus metavar var b end metavar plus metavar var c end metavar suc end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,