define pyk of lemma eqLeq(R) 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 e unicode small q unicode capital l unicode small e unicode small q unicode left parenthesis unicode capital r unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma eqLeq(R) as text unicode start of text unicode small e unicode small q unicode capital l unicode small e unicode small q unicode left parenthesis unicode capital r unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma eqLeq(R) as system Q infer all metavar var rx end metavar indeed all metavar var ry end metavar indeed metavar var rx end metavar == metavar var ry end metavar infer not0 metavar var rx end metavar << metavar var ry end metavar imply metavar var rx end metavar == metavar var ry end metavar end define
define proof of lemma eqLeq(R) 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 metavar var rx end metavar == metavar var ry end metavar infer prop lemma weaken or first modus ponens 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 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 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,