Logiweb aspects of mendelson three two g induction in pyk

Up Help

The predefined "pyk" aspect

define pyk of mendelson three two g induction as text unicode start of text unicode small m unicode small e unicode small n unicode small d unicode small e unicode small l unicode small s unicode small o unicode small n 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 g unicode space unicode small i unicode small n unicode small d unicode small u unicode small c unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of mendelson three two g induction as text unicode start of text unicode capital m unicode small e unicode small n unicode small d unicode small e unicode small l unicode small s unicode small o unicode small n unicode three unicode period unicode two unicode left parenthesis unicode small g unicode right parenthesis unicode capital i unicode small n unicode small d unicode small u unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of mendelson three two g induction as system prime s infer ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) end define

The user defined "the proof aspect" aspect

define proof of mendelson three two g induction as lambda var c dot lambda var x dot proof expand quote system prime s infer ( ( axiom prime s two conclude ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) cut ( ( axiom prime s six conclude ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ ) ) ) cut ( ( ( weakening modus ponens ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ ) ) ) conclude ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ ) ) ) ) cut ( ( ( ( equal transitivity conditioned rule modus ponens ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ ) ) ) ) modus ponens ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) conclude ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) cut ( ( axiom prime s six conclude ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) cut ( ( ( add one modus ponens ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) conclude ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) cut ( ( ( weakening modus ponens ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) conclude ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) cut ( ( ( mendelson three two d conditioned rule modus ponens ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) modus ponens ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano succ ) ) ) ) conclude ( ( ( var t peano var peano succ peano plus ( var r peano var ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) peano imply ( ( var t peano var peano succ peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano succ ) ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define