Logiweb aspects of lemma f2R(Plus) in pyk

Up Help

The predefined "pyk" aspect

define pyk of lemma f2R(Plus) 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 f unicode two unicode capital r unicode left parenthesis unicode capital p unicode small l unicode small u unicode small s unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma f2R(Plus) as text unicode start of text unicode small f unicode two unicode capital r unicode left parenthesis unicode capital p unicode small l unicode small u unicode small s 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 f2R(Plus) as system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed all metavar var fu end metavar indeed all metavar var fv end metavar indeed metavar var fx end metavar +f metavar var fy end metavar sameF metavar var fz end metavar infer R( var fx +f var fy ) == R( metavar var fz end metavar ) end define

The user defined "the proof aspect" aspect

define proof of lemma f2R(Plus) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed all metavar var fu end metavar indeed all metavar var fv end metavar indeed metavar var fx end metavar +f metavar var fy end metavar sameF metavar var fz end metavar infer metavar var fu end metavar in0 R( metavar var fx end metavar +f metavar var fy end metavar ) infer metavar var fv end metavar in0 R( metavar var fz end metavar ) infer 1rule fromInR modus ponens metavar var fu end metavar in0 R( metavar var fx end metavar +f metavar var fy end metavar ) conclude metavar var fu end metavar sameF metavar var fx end metavar +f metavar var fy end metavar cut 1rule fromInR modus ponens metavar var fv end metavar in0 R( metavar var fz end metavar ) conclude metavar var fv end metavar sameF metavar var fz end metavar cut lemma sameFsymmetry modus ponens metavar var fv end metavar sameF metavar var fz end metavar conclude metavar var fz end metavar sameF metavar var fv end metavar cut lemma sameFtransitivity modus ponens metavar var fu end metavar sameF metavar var fx end metavar +f metavar var fy end metavar modus ponens metavar var fx end metavar +f metavar var fy end metavar sameF metavar var fz end metavar conclude metavar var fu end metavar sameF metavar var fz end metavar cut lemma sameFtransitivity modus ponens metavar var fu end metavar sameF metavar var fz end metavar modus ponens metavar var fz end metavar sameF metavar var fv end metavar conclude metavar var fu end metavar sameF metavar var fv end metavar cut all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed all metavar var fu end metavar indeed all metavar var fv end metavar indeed 1rule deduction modus ponens all metavar var fx end metavar indeed all metavar var fy end metavar indeed all metavar var fz end metavar indeed all metavar var fu end metavar indeed all metavar var fv end metavar indeed metavar var fx end metavar +f metavar var fy end metavar sameF metavar var fz end metavar infer metavar var fu end metavar in0 R( metavar var fx end metavar +f metavar var fy end metavar ) infer metavar var fv end metavar in0 R( metavar var fz end metavar ) infer metavar var fu end metavar sameF metavar var fv end metavar conclude metavar var fx end metavar +f metavar var fy end metavar sameF metavar var fz end metavar imply metavar var fu end metavar in0 R( metavar var fx end metavar +f metavar var fy end metavar ) imply metavar var fv end metavar in0 R( metavar var fz end metavar ) imply metavar var fu end metavar sameF metavar var fv end metavar cut metavar var fx end metavar +f metavar var fy end metavar sameF metavar var fz end metavar infer 1rule mp modus ponens metavar var fx end metavar +f metavar var fy end metavar sameF metavar var fz end metavar imply metavar var fu end metavar in0 R( metavar var fx end metavar +f metavar var fy end metavar ) imply metavar var fv end metavar in0 R( metavar var fz end metavar ) imply metavar var fu end metavar sameF metavar var fv end metavar modus ponens metavar var fx end metavar +f metavar var fy end metavar sameF metavar var fz end metavar conclude metavar var fu end metavar in0 R( metavar var fx end metavar +f metavar var fy end metavar ) imply metavar var fv end metavar in0 R( metavar var fz end metavar ) imply metavar var fu end metavar sameF metavar var fv end metavar cut 1rule to==XX modus ponens metavar var fu end metavar in0 R( metavar var fx end metavar +f metavar var fy end metavar ) imply metavar var fv end metavar in0 R( metavar var fz end metavar ) imply metavar var fu end metavar sameF metavar var fv end metavar conclude R( metavar var fx end metavar +f metavar var fy end metavar ) == R( metavar var fz end metavar ) cut axiom plusR conclude R( var fx +f var fy ) == R( metavar var fx end metavar +f metavar var fy end metavar ) cut lemma ==Transitivity modus ponens R( var fx +f var fy ) == R( metavar var fx end metavar +f metavar var fy end metavar ) modus ponens R( metavar var fx end metavar +f metavar var fy end metavar ) == R( metavar var fz end metavar ) conclude R( var fx +f var fy ) == R( metavar var fz end metavar ) end quote state proof state cache var c end expand end define