Logiweb aspects of lemma ==AdditionLeft in pyk

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The predefined "pyk" aspect

define pyk of lemma ==AdditionLeft as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode equal sign unicode equal sign unicode capital a unicode small d unicode small d unicode small i unicode small t unicode small i unicode small o unicode small n unicode capital l unicode small e unicode small f unicode small t unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma ==AdditionLeft as text unicode start of text unicode equal sign unicode equal sign unicode capital a unicode small d unicode small d unicode small i unicode small t unicode small i unicode small o unicode small n unicode capital l unicode small e unicode small f unicode small t unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma ==AdditionLeft as system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed R( metavar var fx end metavar ) == R( metavar var fy end metavar ) infer R( var fx +f var fy ) == R( var fx +f var fy ) end define

The user defined "the proof aspect" aspect

define proof of lemma ==AdditionLeft as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed R( metavar var fx end metavar ) == R( metavar var fy end metavar ) infer lemma ==Addition modus ponens R( metavar var fx end metavar ) == R( metavar var fy end metavar ) conclude R( var fx +f var fy ) == R( var fx +f var fy ) cut lemma plusCommutativity(R) conclude R( var fx +f var fy ) == R( var fx +f var fy ) cut lemma plusCommutativity(R) conclude R( var fx +f var fy ) == R( var fx +f var fy ) cut lemma ==Transitivity modus ponens R( var fx +f var fy ) == R( var fx +f var fy ) modus ponens R( var fx +f var fy ) == R( var fx +f var fy ) conclude R( var fx +f var fy ) == R( var fx +f var fy ) cut lemma ==Transitivity modus ponens R( var fx +f var fy ) == R( var fx +f var fy ) modus ponens R( var fx +f var fy ) == R( var fx +f var fy ) conclude R( var fx +f var fy ) == R( var fx +f var fy ) end quote state proof state cache var c end expand end define