Logiweb aspects of mendelson lemma one eleven d in pyk

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The predefined "pyk" aspect

define pyk of mendelson lemma one eleven d 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 l unicode small e unicode small m unicode small m unicode small a unicode space unicode small o unicode small n unicode small e unicode space unicode small e unicode small l unicode small e unicode small v unicode small e unicode small n unicode space unicode small d unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of mendelson lemma one eleven d 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 backslash unicode space unicode backslash unicode small t unicode small e unicode small x unicode small t unicode small b unicode small f unicode left brace unicode one unicode period unicode one unicode one unicode right brace unicode backslash unicode space unicode small d unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of mendelson lemma one eleven d as system prime s infer all metavar var a end metavar indeed all metavar var b end metavar indeed ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( metavar var b end metavar peano imply metavar var a end metavar ) ) end define

The user defined "the proof aspect" aspect

define proof of mendelson lemma one eleven d 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 ( ( mendelson lemma one eight conclude ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) ) ) cut ( ( axiom prime a three conclude ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( ( ( peano not metavar var a end metavar ) peano imply metavar var b end metavar ) peano imply metavar var a end metavar ) ) ) cut ( ( ( inference axiom prime a one modus ponens ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( ( ( peano not metavar var a end metavar ) peano imply metavar var b end metavar ) peano imply metavar var a end metavar ) ) ) conclude ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( ( ( peano not metavar var a end metavar ) peano imply metavar var b end metavar ) peano imply metavar var a end metavar ) ) ) ) cut ( ( axiom prime a one conclude ( metavar var b end metavar peano imply ( ( peano not metavar var a end metavar ) peano imply metavar var b end metavar ) ) ) cut ( ( ( inference axiom prime a one modus ponens ( metavar var b end metavar peano imply ( ( peano not metavar var a end metavar ) peano imply metavar var b end metavar ) ) ) conclude ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( metavar var b end metavar peano imply ( ( peano not metavar var a end metavar ) peano imply metavar var b end metavar ) ) ) ) cut ( ( ( ( inference inference axiom prime a two modus ponens ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( ( ( peano not metavar var a end metavar ) peano imply metavar var b end metavar ) peano imply metavar var a end metavar ) ) ) ) modus ponens ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) ) ) conclude ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( ( ( peano not metavar var a end metavar ) peano imply metavar var b end metavar ) peano imply metavar var a end metavar ) ) ) cut ( ( ( ( hypothetical mendelson exercise one fourtyseven b modus ponens ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( metavar var b end metavar peano imply ( ( peano not metavar var a end metavar ) peano imply metavar var b end metavar ) ) ) ) modus ponens ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( ( ( peano not metavar var a end metavar ) peano imply metavar var b end metavar ) peano imply metavar var a end metavar ) ) ) conclude ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( metavar var b end metavar peano imply metavar var a end metavar ) ) ) cut ( ( inference mendelson lemma one eight modus ponens ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( metavar var b end metavar peano imply metavar var a end metavar ) ) ) conclude ( ( ( peano not metavar var a end metavar ) peano imply peano not metavar var b end metavar ) peano imply ( metavar var b end metavar peano imply metavar var a end metavar ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define