Logiweb aspects of lemma negative(R) in pyk

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The predefined "pyk" aspect

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

The predefined "tex" aspect

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

The user defined "the statement aspect" aspect

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

The user defined "the proof aspect" aspect

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