Logiweb aspects of hypothetical inference inference mendelson proposition three two c in pyk

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The predefined "pyk" aspect

define pyk of hypothetical inference inference mendelson proposition three two c as text unicode start of text unicode small h unicode small y unicode small p unicode small o unicode small t unicode small h unicode small e unicode small t unicode small i unicode small c unicode small a unicode small l unicode space unicode small i unicode small n unicode small f unicode small e unicode small r unicode small e unicode small n unicode small c unicode small e unicode space unicode small i unicode small n unicode small f unicode small e unicode small r unicode small e unicode small n unicode small c unicode small e unicode space 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 p unicode small r unicode small o unicode small p unicode small o unicode small s unicode small i unicode small t unicode small i 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 c unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of hypothetical inference inference mendelson proposition three two c 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 three unicode period unicode two unicode right brace unicode backslash unicode space unicode small c unicode underscore unicode left brace unicode small i unicode small i unicode small h unicode right brace unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of hypothetical inference inference mendelson proposition three two c as system prime s infer all metavar var h end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed ( ( metavar var h end metavar peano imply ( metavar var a end metavar peano is metavar var b end metavar ) ) infer ( ( metavar var h end metavar peano imply ( metavar var b end metavar peano is metavar var c end metavar ) ) infer ( metavar var h end metavar peano imply ( metavar var a end metavar peano is metavar var c end metavar ) ) ) ) end define

The user defined "the proof aspect" aspect

define proof of hypothetical inference inference mendelson proposition three two c as lambda var c dot lambda var x dot proof expand quote system prime s infer all metavar var h end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed ( ( metavar var h end metavar peano imply ( metavar var a end metavar peano is metavar var b end metavar ) ) infer ( ( metavar var h end metavar peano imply ( metavar var b end metavar peano is metavar var c end metavar ) ) infer ( ( mendelson lemma one eight conclude ( metavar var h end metavar peano imply metavar var h end metavar ) ) cut ( ( mendelson proposition three two c conclude ( ( metavar var a end metavar peano is metavar var b end metavar ) peano imply ( ( metavar var b end metavar peano is metavar var c end metavar ) peano imply ( metavar var a end metavar peano is metavar var c end metavar ) ) ) ) cut ( ( ( inference axiom prime a one modus ponens ( ( metavar var a end metavar peano is metavar var b end metavar ) peano imply ( ( metavar var b end metavar peano is metavar var c end metavar ) peano imply ( metavar var a end metavar peano is metavar var c end metavar ) ) ) ) conclude ( metavar var h end metavar peano imply ( ( metavar var a end metavar peano is metavar var b end metavar ) peano imply ( ( metavar var b end metavar peano is metavar var c end metavar ) peano imply ( metavar var a end metavar peano is metavar var c end metavar ) ) ) ) ) cut ( ( ( ( ( double inference inference axiom prime a two modus ponens ( metavar var h end metavar peano imply ( ( metavar var a end metavar peano is metavar var b end metavar ) peano imply ( ( metavar var b end metavar peano is metavar var c end metavar ) peano imply ( metavar var a end metavar peano is metavar var c end metavar ) ) ) ) ) modus ponens ( metavar var h end metavar peano imply ( metavar var a end metavar peano is metavar var b end metavar ) ) ) modus ponens ( metavar var h end metavar peano imply ( metavar var b end metavar peano is metavar var c end metavar ) ) ) conclude ( metavar var h end metavar peano imply ( metavar var a end metavar peano is metavar var c end metavar ) ) ) cut ( ( inference mendelson lemma one eight modus ponens ( metavar var h end metavar peano imply ( metavar var a end metavar peano is metavar var c end metavar ) ) ) conclude ( metavar var h end metavar peano imply ( metavar var a end metavar peano is metavar var c end metavar ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define