Logiweb aspects of prop three two d hyp rule in pyk

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The predefined "pyk" aspect

define pyk of prop three two d hyp rule as text unicode start of text unicode small p unicode small r unicode small o unicode small p 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 d unicode space unicode small h unicode small y unicode small p unicode space unicode small r unicode small u unicode small l unicode small e unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of prop three two d hyp rule as text unicode start of text unicode backslash unicode small m unicode small a unicode small t unicode small h unicode small i unicode small t unicode left brace 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 space unicode backslash unicode semicolon unicode space unicode three unicode period unicode two unicode left parenthesis unicode small d unicode right parenthesis unicode underscore unicode small h unicode circumflex unicode capital r unicode right brace unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of prop three two d hyp rule as system prime s infer all metavar var h end metavar indeed all metavar var t end metavar indeed all metavar var r end metavar indeed all metavar var s end metavar indeed ( ( metavar var h end metavar peano imply ( metavar var r end metavar peano is metavar var t end metavar ) ) infer ( ( metavar var h end metavar peano imply ( metavar var s end metavar peano is metavar var t end metavar ) ) infer ( metavar var h end metavar peano imply ( metavar var r end metavar peano is metavar var s end metavar ) ) ) ) end define

The user defined "the proof aspect" aspect

define proof of prop three two d hyp rule 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 t end metavar indeed all metavar var r end metavar indeed all metavar var s end metavar indeed ( ( metavar var h end metavar peano imply ( metavar var r end metavar peano is metavar var t end metavar ) ) infer ( ( metavar var h end metavar peano imply ( metavar var s end metavar peano is metavar var t end metavar ) ) infer ( ( prop three two d conclude ( ( metavar var r end metavar peano is metavar var t end metavar ) peano imply ( ( metavar var s end metavar peano is metavar var t end metavar ) peano imply ( metavar var r end metavar peano is metavar var s end metavar ) ) ) ) cut ( ( ( hypothesize modus ponens ( ( metavar var r end metavar peano is metavar var t end metavar ) peano imply ( ( metavar var s end metavar peano is metavar var t end metavar ) peano imply ( metavar var r end metavar peano is metavar var s end metavar ) ) ) ) conclude ( metavar var h end metavar peano imply ( ( metavar var r end metavar peano is metavar var t end metavar ) peano imply ( ( metavar var s end metavar peano is metavar var t end metavar ) peano imply ( metavar var r end metavar peano is metavar var s end metavar ) ) ) ) ) cut ( ( ( ( hypothetical rule prime mp modus ponens ( metavar var h end metavar peano imply ( ( metavar var r end metavar peano is metavar var t end metavar ) peano imply ( ( metavar var s end metavar peano is metavar var t end metavar ) peano imply ( metavar var r end metavar peano is metavar var s end metavar ) ) ) ) ) modus ponens ( metavar var h end metavar peano imply ( metavar var r end metavar peano is metavar var t end metavar ) ) ) conclude ( metavar var h end metavar peano imply ( ( metavar var s end metavar peano is metavar var t end metavar ) peano imply ( metavar var r end metavar peano is metavar var s end metavar ) ) ) ) cut ( ( ( hypothetical rule prime mp modus ponens ( metavar var h end metavar peano imply ( ( metavar var s end metavar peano is metavar var t end metavar ) peano imply ( metavar var r end metavar peano is metavar var s end metavar ) ) ) ) modus ponens ( metavar var h end metavar peano imply ( metavar var s end metavar peano is metavar var t end metavar ) ) ) conclude ( metavar var h end metavar peano imply ( metavar var r end metavar peano is metavar var s end metavar ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define