Logiweb aspects of lemma double hyp in pyk

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The predefined "pyk" aspect

define pyk of lemma double hyp 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 d unicode small o unicode small u unicode small b unicode small l unicode small e unicode space unicode small h unicode small y unicode small p unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma double hyp as text unicode start of text unicode capital d unicode small o unicode small u unicode small b unicode small l unicode small e unicode space unicode capital h unicode small y unicode small p unicode small o unicode small t unicode small h unicode small e unicode small s unicode small i unicode small s unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma double hyp as system prime s infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var h end metavar indeed ( ( metavar var a end metavar peano imply metavar var b end metavar ) infer ( ( metavar var h end metavar peano imply metavar var a end metavar ) peano imply ( metavar var h end metavar peano imply metavar var b end metavar ) ) ) end define

The user defined "the proof aspect" aspect

define proof of lemma double hyp 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 h end metavar indeed ( ( metavar var a end metavar peano imply metavar var b end metavar ) infer ( ( ( lemma prime a one star modus ponens ( metavar var a end metavar peano imply metavar var b end metavar ) ) conclude ( metavar var h end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) cut ( ( lemma prime a two star modus ponens ( metavar var h end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) conclude ( ( metavar var h end metavar peano imply metavar var a end metavar ) peano imply ( metavar var h end metavar peano imply metavar var b end metavar ) ) ) ) ) end quote state proof state cache var c end expand end define