define pyk of lemma base(1/2)Sum(+1) 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 b unicode small a unicode small s unicode small e unicode left parenthesis unicode one unicode slash unicode two unicode right parenthesis unicode capital s unicode small u unicode small m unicode left parenthesis unicode plus sign unicode one unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma base(1/2)Sum(+1) as text unicode start of text unicode capital b unicode capital s unicode left parenthesis unicode plus sign unicode one unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma base(1/2)Sum(+1) as system Q infer all metavar var m end metavar indeed all metavar var n end metavar indeed base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) end define
define proof of lemma base(1/2)Sum(+1) 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 n end metavar indeed lemma +1IsPositive(N) conclude not0 0 <= metavar var n end metavar + 1 imply not0 not0 0 = metavar var n end metavar + 1 cut 1rule base(1/2)Sum positive modus ponens not0 0 <= metavar var n end metavar + 1 imply not0 not0 0 = metavar var n end metavar + 1 conclude base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) cut axiom plusAssociativity conclude metavar var m end metavar + metavar var n end metavar + 1 = metavar var m end metavar + metavar var n end metavar + 1 cut lemma sameExp modus ponens metavar var m end metavar + metavar var n end metavar + 1 = metavar var m end metavar + metavar var n end metavar + 1 conclude 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 cut lemma eqSymmetry modus ponens 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 conclude 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 cut lemma x=x+y-y conclude metavar var n end metavar = metavar var n end metavar + 1 + - 1 cut lemma sameBase(1/2)Sum second modus ponens metavar var n end metavar = metavar var n end metavar + 1 + - 1 conclude base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) = base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) cut lemma eqSymmetry modus ponens base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) = base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) conclude base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) cut lemma addEquations modus ponens 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 modus ponens base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) conclude 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) cut lemma eqTransitivity modus ponens base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) modus ponens 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 + - 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) conclude base(1/2)Sum( metavar var m end metavar , metavar var n end metavar + 1 ) = 1/ 1 + 1 ^ metavar var m end metavar + metavar var n end metavar + 1 + base(1/2)Sum( metavar var m end metavar , metavar var n end metavar ) end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,