Logiweb aspects of lemma tautology one in pyk

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The predefined "pyk" aspect

define pyk of lemma tautology one 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 t unicode small a unicode small u unicode small t unicode small o unicode small l unicode small o unicode small g unicode small y unicode space unicode small o unicode small n unicode small e unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma tautology one as text unicode start of text unicode capital t unicode small a unicode small u unicode small t unicode space unicode one unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma tautology one as system prime 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 peano imply ( metavar var b end metavar peano imply metavar var c end metavar ) ) infer ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) end define

The user defined "the proof aspect" aspect

define proof of lemma tautology one as lambda var c dot lambda var x dot proof expand quote system prime 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 peano imply ( metavar var b end metavar peano imply metavar var c end metavar ) ) infer ( ( axiom prime a two conclude ( ( metavar var a end metavar peano imply ( metavar var b end metavar peano imply metavar var c end metavar ) ) peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( metavar var a end metavar peano imply ( metavar var b end metavar peano imply metavar var c end metavar ) ) peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) modus ponens ( metavar var a end metavar peano imply ( metavar var b end metavar peano imply metavar var c end metavar ) ) ) conclude ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) cut ( ( ( lemma weaken modus ponens ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) conclude ( metavar var b end metavar peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) cut ( ( axiom prime a two conclude ( ( metavar var b end metavar peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) peano imply ( ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) peano imply ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) ) cut ( ( axiom prime a one conclude ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) cut ( ( ( ( lemma mp twice modus ponens ( ( metavar var b end metavar peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) peano imply ( ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) peano imply ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) ) modus ponens ( metavar var b end metavar peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) modus ponens ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) conclude ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define