Logiweb aspects of hypothetical rule prime gen in pyk

Up Help

The predefined "pyk" aspect

define pyk of hypothetical rule prime gen 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 r unicode small u unicode small l unicode small e unicode space unicode small p unicode small r unicode small i unicode small m unicode small e unicode space unicode small g unicode small e unicode small n unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of hypothetical rule prime gen as text unicode start of text unicode newline unicode capital g unicode small e unicode small n unicode apostrophe unicode underscore unicode small h unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of hypothetical rule prime gen as system prime s infer all metavar var h end metavar indeed all metavar var x end metavar indeed all metavar var a end metavar indeed ( peano nonfree quote metavar var x end metavar end quote in quote metavar var h end metavar end quote end nonfree endorse ( ( metavar var h end metavar peano imply metavar var a end metavar ) infer ( metavar var h end metavar peano imply peano all metavar var x end metavar indeed metavar var a end metavar ) ) ) end define

The user defined "the proof aspect" aspect

define proof of hypothetical rule prime gen 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 x end metavar indeed all metavar var a end metavar indeed ( peano nonfree quote metavar var x end metavar end quote in quote metavar var h end metavar end quote end nonfree endorse ( ( metavar var h end metavar peano imply metavar var a end metavar ) infer ( ( ( axiom prime a five modus probans peano nonfree quote metavar var x end metavar end quote in quote metavar var h end metavar end quote end nonfree ) conclude ( ( peano all metavar var x end metavar indeed ( metavar var h end metavar peano imply metavar var a end metavar ) ) peano imply ( metavar var h end metavar peano imply peano all metavar var x end metavar indeed metavar var a end metavar ) ) ) cut ( ( ( rule prime gen modus ponens ( metavar var h end metavar peano imply metavar var a end metavar ) ) conclude peano all metavar var x end metavar indeed ( metavar var h end metavar peano imply metavar var a end metavar ) ) cut ( ( ( rule prime mp modus ponens ( ( peano all metavar var x end metavar indeed ( metavar var h end metavar peano imply metavar var a end metavar ) ) peano imply ( metavar var h end metavar peano imply peano all metavar var x end metavar indeed metavar var a end metavar ) ) ) modus ponens peano all metavar var x end metavar indeed ( metavar var h end metavar peano imply metavar var a end metavar ) ) conclude ( metavar var h end metavar peano imply peano all metavar var x end metavar indeed metavar var a end metavar ) ) ) ) ) ) end quote state proof state cache var c end expand end define