define pyk of lemma negativeToLeft(Less)(1 term) 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 n unicode small e unicode small g unicode small a unicode small t unicode small i unicode small v unicode small e unicode capital t unicode small o unicode capital l unicode small e unicode small f unicode small t unicode left parenthesis unicode capital l unicode small e unicode small s unicode small s unicode right parenthesis unicode left parenthesis unicode one unicode space unicode small t unicode small e unicode small r unicode small m unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma negativeToLeft(Less)(1 term) as text unicode start of text unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small i unicode small v unicode small e unicode capital t unicode small o unicode capital l unicode small e unicode small f unicode small t unicode left parenthesis unicode capital l unicode small e unicode small s unicode small s unicode right parenthesis unicode left parenthesis unicode one unicode space unicode small t unicode small e unicode small r unicode small m unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma negativeToLeft(Less)(1 term) as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed not0 0 <= metavar var x end metavar + - metavar var y end metavar imply not0 not0 0 = metavar var x end metavar + - metavar var y end metavar infer not0 metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar end define
define proof of lemma negativeToLeft(Less)(1 term) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed not0 0 <= metavar var x end metavar + - metavar var y end metavar imply not0 not0 0 = metavar var x end metavar + - metavar var y end metavar infer lemma lessAddition modus ponens not0 0 <= metavar var x end metavar + - metavar var y end metavar imply not0 not0 0 = metavar var x end metavar + - metavar var y end metavar conclude not0 0 + metavar var y end metavar <= metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar imply not0 not0 0 + metavar var y end metavar = metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar cut lemma plus0Left conclude 0 + metavar var y end metavar = metavar var y end metavar cut lemma subLessLeft modus ponens 0 + metavar var y end metavar = metavar var y end metavar modus ponens not0 0 + metavar var y end metavar <= metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar imply not0 not0 0 + metavar var y end metavar = metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar conclude not0 metavar var y end metavar <= metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar cut lemma three2threeTerms conclude metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar cut lemma x=x+y-y conclude metavar var x end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar conclude metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar = metavar var x end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar = metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar modus ponens metavar var x end metavar + metavar var y end metavar + - metavar var y end metavar = metavar var x end metavar conclude metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar = metavar var x end metavar cut lemma subLessRight modus ponens metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar = metavar var x end metavar modus ponens not0 metavar var y end metavar <= metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar + - metavar var y end metavar + metavar var y end metavar conclude not0 metavar var y end metavar <= metavar var x end metavar imply not0 not0 metavar var y end metavar = metavar var x end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,