Logiweb aspects of lemma <<==Antisymmetry in pyk

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The predefined "pyk" aspect

define pyk of lemma <<==Antisymmetry as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode less than unicode less than unicode equal sign unicode equal sign unicode capital a unicode small n unicode small t unicode small i unicode small s unicode small y unicode small m unicode small m unicode small e unicode small t unicode small r unicode small y unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma <<==Antisymmetry as text unicode start of text unicode less than unicode less than unicode equal sign unicode equal sign unicode capital a unicode small n unicode small t unicode small i unicode small s unicode small y unicode small m unicode small m unicode small e unicode small t unicode small r unicode small y unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma <<==Antisymmetry as system Q infer all metavar var rx end metavar indeed all metavar var ry end metavar indeed not0 metavar var rx end metavar << metavar var ry end metavar imply metavar var rx end metavar == metavar var ry end metavar infer not0 metavar var ry end metavar << metavar var rx end metavar imply metavar var ry end metavar == metavar var rx end metavar infer metavar var rx end metavar == metavar var ry end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma <<==Antisymmetry as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var rx end metavar indeed all metavar var ry end metavar indeed not0 metavar var rx end metavar << metavar var ry end metavar imply metavar var rx end metavar == metavar var ry end metavar infer not0 metavar var ry end metavar << metavar var rx end metavar imply metavar var ry end metavar == metavar var rx end metavar infer 1rule repetition modus ponens not0 metavar var rx end metavar << metavar var ry end metavar imply metavar var rx end metavar == metavar var ry end metavar conclude not0 metavar var rx end metavar << metavar var ry end metavar imply metavar var rx end metavar == metavar var ry end metavar cut 1rule repetition modus ponens not0 metavar var ry end metavar << metavar var rx end metavar imply metavar var ry end metavar == metavar var rx end metavar conclude not0 metavar var ry end metavar << metavar var rx end metavar imply metavar var ry end metavar == metavar var rx end metavar cut prop lemma expand disjuncts modus ponens not0 metavar var rx end metavar << metavar var ry end metavar imply metavar var rx end metavar == metavar var ry end metavar modus ponens not0 metavar var ry end metavar << metavar var rx end metavar imply metavar var ry end metavar == metavar var rx end metavar conclude not0 metavar var rx end metavar == metavar var ry end metavar imply not0 metavar var ry end metavar == metavar var rx end metavar imply not0 metavar var rx end metavar << metavar var ry end metavar imply not0 metavar var ry end metavar << metavar var rx end metavar cut prop lemma auto imply conclude metavar var rx end metavar == metavar var ry end metavar imply metavar var rx end metavar == metavar var ry end metavar cut all metavar var rx end metavar indeed all metavar var ry end metavar indeed metavar var ry end metavar == metavar var rx end metavar infer lemma ==Symmetry modus ponens metavar var ry end metavar == metavar var rx end metavar conclude metavar var rx end metavar == metavar var ry end metavar cut 1rule deduction modus ponens all metavar var rx end metavar indeed all metavar var ry end metavar indeed metavar var ry end metavar == metavar var rx end metavar infer metavar var rx end metavar == metavar var ry end metavar conclude metavar var ry end metavar == metavar var rx end metavar imply metavar var rx end metavar == metavar var ry end metavar cut all metavar var rx end metavar indeed all metavar var ry end metavar indeed not0 metavar var rx end metavar << metavar var ry end metavar imply not0 metavar var ry end metavar << metavar var rx end metavar infer prop lemma first conjunct modus ponens not0 metavar var rx end metavar << metavar var ry end metavar imply not0 metavar var ry end metavar << metavar var rx end metavar conclude metavar var rx end metavar << metavar var ry end metavar cut 1rule from<