Logiweb aspects of prop three two e two in pyk

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The predefined "pyk" aspect

define pyk of prop three two e two 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 e unicode space unicode small t unicode small w unicode small o unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of prop three two e two as text unicode start of text unicode newline unicode capital p unicode small r unicode small o unicode small p unicode backslash unicode space unicode three unicode period unicode two unicode small e unicode underscore unicode two unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of prop three two e two as system 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 equal metavar var b end metavar ) imply ( ( metavar var a end metavar plus metavar var c end metavar ) equal ( metavar var b end metavar plus metavar var c end metavar ) ) ) imply ( ( metavar var a end metavar equal metavar var b end metavar ) imply ( ( metavar var a end metavar plus ( metavar var c end metavar suc ) ) equal ( metavar var b end metavar plus ( metavar var c end metavar suc ) ) ) ) ) end define

The user defined "the proof aspect" aspect

define proof of prop three two e two as lambda var c dot lambda var x dot proof expand quote system s infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed ( ( 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 equal metavar var b end metavar ) imply ( ( metavar var a end metavar plus metavar var c end metavar ) equal ( metavar var b end metavar plus metavar var c end metavar ) ) ) infer ( ( metavar var a end metavar equal metavar var b end metavar ) infer ( ( ( ( rule mp modus ponens ( ( metavar var a end metavar equal metavar var b end metavar ) imply ( ( metavar var a end metavar plus metavar var c end metavar ) equal ( metavar var b end metavar plus metavar var c end metavar ) ) ) ) modus ponens ( metavar var a end metavar equal metavar var b end metavar ) ) conclude ( ( metavar var a end metavar plus metavar var c end metavar ) equal ( metavar var b end metavar plus metavar var c end metavar ) ) ) cut ( ( ( axiom s two modus ponens ( ( metavar var a end metavar plus metavar var c end metavar ) equal ( metavar var b end metavar plus metavar var c end metavar ) ) ) conclude ( ( metavar var a end metavar plus metavar var c end metavar ) suc equal ( ( metavar var b end metavar plus metavar var c end metavar ) suc ) ) ) cut ( ( axiom s six conclude ( ( metavar var a end metavar plus ( metavar var c end metavar suc ) ) equal ( ( metavar var a end metavar plus metavar var c end metavar ) suc ) ) ) cut ( ( ( ( prop three two c modus ponens ( ( metavar var a end metavar plus ( metavar var c end metavar suc ) ) equal ( ( metavar var a end metavar plus metavar var c end metavar ) suc ) ) ) modus ponens ( ( metavar var a end metavar plus metavar var c end metavar ) suc equal ( ( metavar var b end metavar plus metavar var c end metavar ) suc ) ) ) conclude ( ( metavar var a end metavar plus ( metavar var c end metavar suc ) ) equal ( ( metavar var b end metavar plus metavar var c end metavar ) suc ) ) ) cut ( ( axiom s six conclude ( ( metavar var b end metavar plus ( metavar var c end metavar suc ) ) equal ( ( metavar var b end metavar plus metavar var c end metavar ) suc ) ) ) cut ( ( ( prop three two d modus ponens ( ( metavar var a end metavar plus ( metavar var c end metavar suc ) ) equal ( ( metavar var b end metavar plus metavar var c end metavar ) suc ) ) ) modus ponens ( ( metavar var b end metavar plus ( metavar var c end metavar suc ) ) equal ( ( metavar var b end metavar plus metavar var c end metavar ) suc ) ) ) conclude ( ( metavar var a end metavar plus ( metavar var c end metavar suc ) ) equal ( metavar var b end metavar plus ( metavar var c end metavar suc ) ) ) ) ) ) ) ) ) ) ) ) cut ( ( deduction modus ponens 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 equal metavar var b end metavar ) imply ( ( metavar var a end metavar plus metavar var c end metavar ) equal ( metavar var b end metavar plus metavar var c end metavar ) ) ) infer ( ( metavar var a end metavar equal metavar var b end metavar ) infer ( ( metavar var a end metavar plus ( metavar var c end metavar suc ) ) equal ( metavar var b end metavar plus ( metavar var c end metavar suc ) ) ) ) ) ) conclude ( ( ( metavar var a end metavar equal metavar var b end metavar ) imply ( ( metavar var a end metavar plus metavar var c end metavar ) equal ( metavar var b end metavar plus metavar var c end metavar ) ) ) imply ( ( metavar var a end metavar equal metavar var b end metavar ) imply ( ( metavar var a end metavar plus ( metavar var c end metavar suc ) ) equal ( metavar var b end metavar plus ( metavar var c end metavar suc ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define