define pyk of lemma negative(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 n unicode small e unicode small g unicode small a unicode small t unicode small i unicode small v unicode small e unicode left parenthesis unicode capital r unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma negative(R) 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 left parenthesis unicode capital r unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma negative(R) as system Q infer all metavar var m end metavar indeed all metavar var fx end metavar indeed R( var fx +f var fy ) == R( 0f ) end define
define proof of lemma negative(R) 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 fx end metavar indeed axiom plusF conclude [ metavar var fx end metavar +f -f metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] + [ -f metavar var fx end metavar ; metavar var m end metavar ] cut axiom minusF conclude [ -f metavar var fx end metavar ; metavar var m end metavar ] = - [ metavar var fx end metavar ; metavar var m end metavar ] cut lemma eqAdditionLeft modus ponens [ -f metavar var fx end metavar ; metavar var m end metavar ] = - [ metavar var fx end metavar ; metavar var m end metavar ] conclude [ metavar var fx end metavar ; metavar var m end metavar ] + [ -f metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] cut axiom negative conclude [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] = 0 cut axiom 0f conclude [ 0f ; metavar var m end metavar ] = 0 cut lemma eqSymmetry modus ponens [ 0f ; metavar var m end metavar ] = 0 conclude 0 = [ 0f ; metavar var m end metavar ] cut lemma eqTransitivity5 modus ponens [ metavar var fx end metavar +f -f metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] + [ -f metavar var fx end metavar ; metavar var m end metavar ] modus ponens [ metavar var fx end metavar ; metavar var m end metavar ] + [ -f metavar var fx end metavar ; metavar var m end metavar ] = [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] modus ponens [ metavar var fx end metavar ; metavar var m end metavar ] + - [ metavar var fx end metavar ; metavar var m end metavar ] = 0 modus ponens 0 = [ 0f ; metavar var m end metavar ] conclude [ metavar var fx end metavar +f -f metavar var fx end metavar ; metavar var m end metavar ] = [ 0f ; metavar var m end metavar ] cut 1rule to=f modus ponens [ metavar var fx end metavar +f -f metavar var fx end metavar ; metavar var m end metavar ] = [ 0f ; metavar var m end metavar ] conclude metavar var fx end metavar +f -f metavar var fx end metavar =f 0f cut lemma =f to sameF modus ponens metavar var fx end metavar +f -f metavar var fx end metavar =f 0f conclude metavar var fx end metavar +f -f metavar var fx end metavar sameF 0f cut lemma f2R(Plus) modus ponens metavar var fx end metavar +f -f metavar var fx end metavar sameF 0f conclude R( var fx +f var fy ) == R( 0f ) cut 1rule repetition modus ponens R( var fx +f var fy ) == R( 0f ) conclude R( var fx +f var fy ) == R( 0f ) end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,