Logiweb aspects of double inference inference axiom prime a two in pyk

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The predefined "pyk" aspect

define pyk of double inference inference axiom prime a two as text unicode start of text unicode small d unicode small o unicode small u unicode small b unicode small l 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 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 a unicode small x unicode small i unicode small o unicode small m unicode space unicode small p unicode small r unicode small i unicode small m unicode small e unicode space unicode small a unicode space unicode small t unicode small w unicode small o unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of double inference inference axiom prime a two as text unicode start of text unicode capital a unicode two unicode apostrophe unicode underscore unicode left brace unicode small i unicode small i unicode small d unicode right brace unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of double inference inference axiom prime a two 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 all metavar var d end metavar indeed ( ( metavar var a end metavar peano imply ( metavar var b end metavar peano imply ( metavar var c end metavar peano imply metavar var d end metavar ) ) ) infer ( ( metavar var a end metavar peano imply metavar var b end metavar ) infer ( ( metavar var a end metavar peano imply metavar var c end metavar ) infer ( metavar var a end metavar peano imply metavar var d end metavar ) ) ) ) end define

The user defined "the proof aspect" aspect

define proof of double inference inference axiom prime a two 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 all metavar var d end metavar indeed ( ( metavar var a end metavar peano imply ( metavar var b end metavar peano imply ( metavar var c end metavar peano imply metavar var d end metavar ) ) ) infer ( ( metavar var a end metavar peano imply metavar var b end metavar ) infer ( ( metavar var a end metavar peano imply metavar var c end metavar ) infer ( ( ( ( inference inference axiom prime a two 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 d end metavar ) ) ) ) modus ponens ( metavar var a end metavar peano imply metavar var b end metavar ) ) conclude ( metavar var a end metavar peano imply ( metavar var c end metavar peano imply metavar var d end metavar ) ) ) cut ( ( ( inference inference axiom prime a two modus ponens ( metavar var a end metavar peano imply ( metavar var c end metavar peano imply metavar var d end metavar ) ) ) modus ponens ( metavar var a end metavar peano imply metavar var c end metavar ) ) conclude ( metavar var a end metavar peano imply metavar var d end metavar ) ) ) ) ) ) end quote state proof state cache var c end expand end define