Logiweb aspects of lemma l three two a in pyk

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The predefined "pyk" aspect

define pyk of lemma l three two a as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small l 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 a unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma l three two a as text unicode start of text unicode newline unicode capital l unicode three unicode period unicode two unicode left parenthesis unicode small a unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma l three two a as system s infer ( var x peano var peano is ( var x peano var ) ) end define

The user defined "the proof aspect" aspect

define proof of lemma l three two a as lambda var c dot lambda var x dot proof expand quote system s infer ( ( axiom s five conclude ( ( var a peano var peano plus peano zero ) peano is ( var a peano var ) ) ) cut ( ( ( rule gen modus ponens ( ( var a peano var peano plus peano zero ) peano is ( var a peano var ) ) ) conclude peano all var a peano var indeed ( ( var a peano var peano plus peano zero ) peano is ( var a peano var ) ) ) cut ( ( ( axiom a four at ( var x peano var ) ) conclude ( ( peano all var a peano var indeed ( ( var a peano var peano plus peano zero ) peano is ( var a peano var ) ) ) peano imply ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) ) ) cut ( ( ( ( rule mp modus ponens ( ( peano all var a peano var indeed ( ( var a peano var peano plus peano zero ) peano is ( var a peano var ) ) ) peano imply ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) ) ) modus ponens peano all var a peano var indeed ( ( var a peano var peano plus peano zero ) peano is ( var a peano var ) ) ) conclude ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) ) cut ( ( axiom s one conclude ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var c peano var ) ) peano imply ( var b peano var peano is ( var c peano var ) ) ) ) ) cut ( ( ( rule gen modus ponens ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var c peano var ) ) peano imply ( var b peano var peano is ( var c peano var ) ) ) ) ) conclude peano all var c peano var indeed ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var c peano var ) ) peano imply ( var b peano var peano is ( var c peano var ) ) ) ) ) cut ( ( ( axiom a four at ( var x peano var ) ) conclude ( ( peano all var c peano var indeed ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var c peano var ) ) peano imply ( var b peano var peano is ( var c peano var ) ) ) ) ) peano imply ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var b peano var peano is ( var x peano var ) ) ) ) ) ) cut ( ( ( ( rule mp modus ponens ( ( peano all var c peano var indeed ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var c peano var ) ) peano imply ( var b peano var peano is ( var c peano var ) ) ) ) ) peano imply ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var b peano var peano is ( var x peano var ) ) ) ) ) ) modus ponens peano all var c peano var indeed ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var c peano var ) ) peano imply ( var b peano var peano is ( var c peano var ) ) ) ) ) conclude ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var b peano var peano is ( var x peano var ) ) ) ) ) cut ( ( ( rule gen modus ponens ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var b peano var peano is ( var x peano var ) ) ) ) ) conclude peano all var b peano var indeed ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var b peano var peano is ( var x peano var ) ) ) ) ) cut ( ( ( axiom a four at ( var x peano var ) ) conclude ( ( peano all var b peano var indeed ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var b peano var peano is ( var x peano var ) ) ) ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) ) cut ( ( ( ( rule mp modus ponens ( ( peano all var b peano var indeed ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var b peano var peano is ( var x peano var ) ) ) ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) ) modus ponens peano all var b peano var indeed ( ( var a peano var peano is ( var b peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var b peano var peano is ( var x peano var ) ) ) ) ) conclude ( ( var a peano var peano is ( var x peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) cut ( ( ( rule gen modus ponens ( ( var a peano var peano is ( var x peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) conclude peano all var a peano var indeed ( ( var a peano var peano is ( var x peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) cut ( ( ( axiom a four at ( var x peano var peano plus peano zero ) ) conclude ( ( peano all var a peano var indeed ( ( var a peano var peano is ( var x peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) peano imply ( ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) peano imply ( ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) ) cut ( ( ( ( rule mp modus ponens ( ( peano all var a peano var indeed ( ( var a peano var peano is ( var x peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) peano imply ( ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) peano imply ( ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) ) modus ponens peano all var a peano var indeed ( ( var a peano var peano is ( var x peano var ) ) peano imply ( ( var a peano var peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) conclude ( ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) peano imply ( ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) cut ( ( ( ( rule mp modus ponens ( ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) peano imply ( ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) ) modus ponens ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) ) conclude ( ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) cut ( ( ( rule mp modus ponens ( ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) peano imply ( var x peano var peano is ( var x peano var ) ) ) ) modus ponens ( ( var x peano var peano plus peano zero ) peano is ( var x peano var ) ) ) conclude ( var x peano var peano is ( var x peano var ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define