Logiweb aspects of weakening in pyk

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The predefined "pyk" aspect

define pyk of weakening as text unicode start of text unicode small w unicode small e unicode small a unicode small k unicode small e unicode small n unicode small i unicode small n unicode small g unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of weakening as text unicode start of text unicode capital w unicode small e unicode small a unicode small k unicode small e unicode small n unicode small i unicode small n unicode small g unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of weakening as system prime s infer all metavar var a end metavar indeed all metavar var b end metavar indeed ( metavar var a end metavar infer ( metavar var b end metavar peano imply metavar var a end metavar ) ) end define

The user defined "the proof aspect" aspect

define proof of weakening 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 ( metavar var a end metavar infer ( ( axiom prime a one conclude ( metavar var a end metavar peano imply ( metavar var b end metavar peano imply metavar var a 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 ) ) ) modus ponens metavar var a end metavar ) conclude ( metavar var b end metavar peano imply metavar var a end metavar ) ) ) ) end quote state proof state cache var c end expand end define