Logiweb aspects of lemma thirdGeqSeries in pyk

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The predefined "pyk" aspect

define pyk of lemma thirdGeqSeries as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small t unicode small h unicode small i unicode small r unicode small d unicode capital g unicode small e unicode small q unicode capital s unicode small e unicode small r unicode small i unicode small e unicode small s unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma thirdGeqSeries as text unicode start of text unicode capital t unicode small h unicode small i unicode small r unicode small d unicode capital g unicode small e unicode small q unicode capital s unicode small e unicode small r unicode small i unicode small e unicode small s unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma thirdGeqSeries as system Q infer all metavar var m end metavar indeed all metavar var ep end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed all metavar var fu end metavar indeed all metavar var rx end metavar indeed all metavar var ry end metavar indeed all metavar var rz end metavar indeed all metavar var ru end metavar indeed metavar var rx end metavar << metavar var ry end metavar infer metavar var rz end metavar << metavar var ru end metavar infer metavar var fx end metavar in0 metavar var rx end metavar infer metavar var fy end metavar in0 metavar var ry end metavar infer metavar var fz end metavar in0 metavar var rz end metavar infer metavar var fu end metavar in0 metavar var ru end metavar infer not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar infer existential var var c end var <= metavar var m end metavar infer not0 [ metavar var fx end metavar ; metavar var m end metavar ] <= [ metavar var fy end metavar ; metavar var m end metavar ] + - metavar var ep end metavar imply not0 [ metavar var fz end metavar ; metavar var m end metavar ] <= [ metavar var fu end metavar ; metavar var m end metavar ] + - metavar var ep end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma thirdGeqSeries as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var m end metavar indeed all metavar var ep end metavar indeed all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed all metavar var fu end metavar indeed all metavar var rx end metavar indeed all metavar var ry end metavar indeed all metavar var rz end metavar indeed all metavar var ru end metavar indeed metavar var rx end metavar << metavar var ry end metavar infer metavar var rz end metavar << metavar var ru end metavar infer metavar var fx end metavar in0 metavar var rx end metavar infer metavar var fy end metavar in0 metavar var ry end metavar infer metavar var fz end metavar in0 metavar var rz end metavar infer metavar var fu end metavar in0 metavar var ru end metavar infer not0 0 <= metavar var ep end metavar imply not0 not0 0 = metavar var ep end metavar infer existential var var c end var <= metavar var m end metavar infer 1rule from<