Logiweb aspects of mendelson tautology a in pyk

Up Help

The predefined "pyk" aspect

define pyk of mendelson tautology a as text unicode start of text 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 t unicode small a unicode small u unicode small t unicode small o unicode small l unicode small o unicode small g unicode small y unicode space unicode small a unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of mendelson tautology a as text unicode start of text unicode capital m unicode backslash unicode space unicode capital t unicode small a unicode small u unicode small t unicode small o unicode small l unicode small o unicode small g unicode small y unicode backslash unicode space unicode capital a unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of mendelson tautology a 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 ( ( metavar var a end metavar peano imply ( metavar var b end metavar peano imply metavar var c end metavar ) ) infer ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) end define

The user defined "the proof aspect" aspect

define proof of mendelson tautology a 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 ( ( metavar var a end metavar peano imply ( metavar var b end metavar peano imply metavar var c end metavar ) ) infer ( ( axiom prime a two conclude ( ( metavar var a end metavar peano imply ( metavar var b end metavar peano imply metavar var c end metavar ) ) peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) cut ( ( ( ( rule prime mp 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 a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) modus ponens ( metavar var a end metavar peano imply ( metavar var b end metavar peano imply metavar var c end metavar ) ) ) conclude ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) cut ( ( axiom prime a one conclude ( ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) peano imply ( metavar var b end metavar peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) peano imply ( metavar var b end metavar peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) ) modus ponens ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) conclude ( metavar var b end metavar peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) cut ( ( axiom prime a two conclude ( ( metavar var b end metavar peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) peano imply ( ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) peano imply ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( metavar var b end metavar peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) peano imply ( ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) peano imply ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) ) modus ponens ( metavar var b end metavar peano imply ( ( metavar var a end metavar peano imply metavar var b end metavar ) peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) conclude ( ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) peano imply ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) cut ( ( axiom prime a one conclude ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) cut ( ( ( rule prime mp modus ponens ( ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) peano imply ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) modus ponens ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) conclude ( metavar var b end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define