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Lemma dependency for Specification cyclic

A lemma (entry) may depend on lemmas (entries) below its position, but never on lemmas above its position. This means the list is a topological order of the dependency graph. An entry 'all subs proved' means that all used lemmas are (transitively) proved.

Name: Status: Subs proved? Used:
junkref-update-equivprovedall subs proved pathex-array, pathex-class, pathex-one, pathex-not-is-validref-01, junkref-update,
pathex-putbar-02provedall subs proved pathex-putbar-01,
junkref-updateprovedall subs proved nopathex-update, junkref-put-nopathex,
pathex-putbar-01provedall subs proved pathex-putbar-03,
validref-nopathex-putprovedall subs proved junkref-put-nopathex-equiv-01,
junkref-put-nopathex-equiv-01provedall subs proved junkrefs-put-nopathex-equiv, junkrefs-put-nopathex,
pathex-putbar-03provedall subs proved pathex-putbyteval,
nopathex-updateprovedall subs proved junkref-put-nopathex, pathex-put-last,
cyclic-put-nopathexprovedall subs proved validrefs-nopathex-01, validrefs-not, pathex-put-last, validrefs-nopathex, pathex-one, validrefs-put-notin, cyclic-def-shortest,
cyclic-putbarprovedall subs proved cyclic-putbyte-01,
cyclic-putbar-02provedall subs proved cyclic-putbar-01,
cyclic-putbar-03provedall subs proved cyclic-putbar-01,
junkref-put-nopathexplus-equivprovedall subs proved junkrefs-put-nopathexplus-equiv,
pathex-levelsubset-equivprovedall subs proved pathex-levelsubset, pathex-levelsubset-01,
cyclic-putbyte-01provedall subs proved validrefs-putbyte, cyclic-def-shortest, cyclic-def-simple, cyclic-putbyte,
cyclic-putbar-01provedall subs proved cyclic-putbar-04,
junkrefs-put-nopathex-equivprovedall subs proved pathex-array, pathex-class, pathex-one, junkrefs-put-nopathex,
junkrefs-put-nopathexplus-equivprovedall subs proved validrefs-array, validrefs-null-02, validrefs-sametype, validrefs-superclass, validrefs-class, step-exists-def, validrefs-one, pathex-plus-def, pathexplus-pathex, junkrefs-put-nopathex,
junkref-put-nopathexprovedall subs proved junkrefs-put-nopathex,
pathex-put-lastprovedall subs proved validrefs-put-last, pathex-one, pathex-def-nodups,
pathex-levelsubset-01provedall subs proved validrefs-levelsubset-01, pathex-def-simple, pathex-one, pathex-def-nodups,
pathex-putbytevalprovedall subs proved pathex-putbyteval-01,
pathex-putshortfield-01provedall subs proved pathex-putshortfield,
pathex-putbyte-field-01provedall subs proved pathex-putbyte-field,
pathex-putbarprovedall subs proved pathex-putbyte,
pathex-put-pathex-array-refvalprovedall subs proved validrefs-null-02, pathex-array, pathex-trans, validrefs-postfix, pathex-def-simple, validrefs-one, pathex-not-is-validref-01, pathex-validrefs-in, validrefs-is-junk, validrefs-array, validrefs-put-notin, pathex-not-is-validref-02, pathex-one, pathex-def-nodups,
pathex-put-cyclicprovedall subs proved validrefs-primtype, validrefs-superclass, validrefs-put-notin-02, validrefs-is-junk, validrefs-postfix, validrefs-one, validrefs-class, pathex-one, pathex-def-nodups, cyclic-def-simple,
pathex-junkref-02provedall subs proved pathex-junkref-01,
cyclic-put-statfield-01provedall subs proved validrefs-sametype, validrefs-null-02, validrefs-put-statfield, cyclic-def-simple, cyclic-put-statfield,
pathex-putshortfieldprovedall subs proved validrefs-putshort-field, pathex-one, pathex-def,
pathex-putbyteval-01provedall subs proved validrefs-putbyte-01, pathex-one, pathex-def,
pathex-putbyte-fieldprovedall subs proved validrefs-putbyte-field, pathex-one, pathex-def,
pathex-putbyteprovedall subs proved validrefs-putbyte, validrefs-putbyte-01, pathex-def-simple,
pathex-def-nodupsprovedall subs proved validrefs-delcycle-01, validrefs-nodups-01, pathex-def-simple,
pathex-junkref-01provedall subs proved pathex-junkref,
junkrefs-put-nopathexprovedall subs proved pathex-array, pathex-class, pathex-one,
cyclic-putbyteprovedall subs proved validrefs-putbyte-01, cyclic-def-simple,
cyclic-putbar-04provedall subs proved validrefs-putbar, cyclic-def,
cyclic-put-statfieldprovedall subs proved cyclic-not-null, validrefs-null-02, validrefs-put-statfield, cyclic-def-simple,
validrefs-nopathex-01provedall subs proved validrefs-nopathex,
cyclic-addobjprovedall subs proved validrefs-one, validrefs-type, validrefs-sametype, validrefs-addobj, validrefs-addobj-junkref, cyclic-not-null, validrefs-null-02, validrefs-class, validrefs-is-junk, validrefs-null, cyclic-def-simple,
cyclic-addobj-other-01provedall subs proved validrefs-newref, validrefs-addobj-notin, cyclic-def-simple, cyclic-addobj-other,
cyclic-addrefarrayprovedall subs proved cyclic-not-null, validrefs-null-02, validrefs-sametype, validrefs-addarray, validrefs-addarray-junkref, validrefs-array, validrefs-is-junk, cyclic-def-simple,
cyclic-put-badarrayfieldprovedall subs proved validrefs-put-badarrayfield-01, validrefs-put-badarrayfield, cyclic-def-shortest,
cyclic-put-badclassfieldprovedall subs proved validrefs-put-badclassfield-01, validrefs-put-badclassfield, cyclic-def-shortest,
cyclic-putbar-05provedall subs proved validrefs-putbar, cyclic-def,
exvalidrefsprovedall subs proved validrefs-delete-01, validrefs-delete, validrefs-del-junkrefs, validrefs-one, cyclic-def-simple, validrefs-null-01, validrefs-class,
exvalidrefs-03provedall subs proved validrefs-null-01, validrefs-delete-01, validrefs-del-junkrefs, validrefs-one, validrefs-class, cyclic-def-simple,
exvalidrefs-maxlengthprovedall subs proved validrefs-del, validrefs-delete-02, validrefs-array, validrefs-delete, validrefs-newref, validrefs-del-junkrefs, validrefs-delete-01, validrefs-class, cyclic-def-simple, validrefs-one, validrefs-null-01, cyclic-not-null,
exvalidrefs-nodupsprovedall subs proved validrefs-null-01, validrefs-delete-01, validrefs-del-junkrefs, validrefs-one, validrefs-class, cyclic-def-simple,
okarray-put-nopath-01provedall subs proved okarray-put-nopath, pathex-lookup-put-other,
pathex-no-newrefprovedall subs proved pathex-not-is-validref,
pathex-put-nopathexprovedall subs proved validrefs-sametype, pathex-array, validrefs-array, pathex-null, pathex-class, validrefs-null-02, validrefs-sametype-03, pathex-one, validrefs-class, validrefs-null, validrefs-is-junk, pathex-def-simple,
pathex-putstatfield-01provedall subs proved pathex-putstatfield,
pathex-subset-equivprovedall subs proved pathex-subset-02, validrefs-subset-equiv, pathex-one, pathex-def,
validrefs-bytearray-01provedall subs proved validrefs-bytearray, validrefs-empty,
cyclic-addobj-otherprovedall subs proved validrefs-addobj-junkref, validrefs-addobj, cyclic-def-simple,
validrefs-putbarprovedall subs proved validrefs-null-01, validrefs-primtype-01, validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk, validrefs-empty,
cyclic-def-shortestprovedall subs proved validrefs-prefix, cyclic-def-simple,
cyclic-not-nullprovedall subs proved validrefs-null-02, validrefs-empty, cyclic-def-simple,
validrefs-delete-01provedall subs proved validrefs-superclass, validrefs-delete,
okarray-put-nopathprovedall subs proved pathex-one,
pathex-lookup-put-otherprovedall subs proved pathex-one,
validrefs-nodups-01provedall subs proved validrefs-delcycle-01,
pathex-junkrefprovedall subs proved validrefs-junkrefs-append, pathex-def-simple,
pathex-not-is-validrefprovedall subs proved validrefs-not-in, validrefs-one, pathex-def-simple,
pathex-classprovedall subs proved validrefs-superclass, validrefs-null-01, validrefs-sametype, validrefs-null, validrefs-is-junk, validrefs-class, pathex-def-simple,
pathex-arrayprovedall subs proved validrefs-superclass, validrefs-null-01, validrefs-null-02, validrefs-sametype, validrefs-is-junk, validrefs-array, pathex-def-simple,
pathex-transprovedall subs proved validrefs-trans, pathex-def,
pathex-not-is-validref-01provedall subs proved validrefs-not-in-01, pathex-def-simple,
validrefs-putbyte-fieldprovedall subs proved validrefs-primtype-01, validrefs-one, validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk,
validrefs-putbyte-01provedall subs proved validrefs-primtype-01, validrefs-one, validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk, validrefs-empty,
validrefs-putshort-fieldprovedall subs proved validrefs-primtype-02, validrefs-one, validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk,
pathex-putstatfieldprovedall subs proved validrefs-put-statfield, validrefs-one, pathex-one, pathex-def,
pathex-subset-02provedall subs proved pathex-subset,
validrefs-bytearrayprovedall subs proved validrefs-one, validrefs-primtype-01, validrefs-array, validrefs-is-junk, validrefs-null,
validrefs-nopathexprovedall subs proved validrefs-prefix, pathex-def-simple, validrefs-sametype,
validrefs-subset-equiv-01provedall subs proved validrefs-subset-equiv,
validrefs-putbar-01provedall subs proved validrefs-one, validrefs-primtype-01, validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk,
validrefs-nodupsprovedall subs proved validrefs-contains-null, validrefs-null-01, validrefs-delcycle, validrefs-null-02,
validrefs-applast-class-nullprovedall subs proved validrefs-null-01, validrefs-class, validrefs-append-01,
validrefs-applast-classprovedall subs proved validrefs-one, validrefs-class, validrefs-append-01,
validrefs-applast-array-nullprovedall subs proved validrefs-null-01, validrefs-array, validrefs-append-01,
validrefs-applast-arrayprovedall subs proved validrefs-one, validrefs-array, validrefs-append-01,
validref-nopath-supersetprovedall subs proved validrefs-subset-notnew, validrefs-one, pathex-def,
pathex-subset-01provedall subs proved pathex-subset,
pathex-put-array-badindexprovedall subs proved validrefs-put-array-badindex, pathex-def-simple,
pathex-null-01provedall subs proved pathex-one, pathex-null,
pathex-noreftypeprovedall subs proved validrefs-postfix, validrefs-primtype, pathex-def-simple,
pathex-addobjprovedall subs proved validrefs-superclass, validrefs-subtype, validrefs-addobj-01, pathex-def,
cyclic-subset-01provedall subs proved validrefs-subset-01, validrefs-null-02, cyclic-def-simple,
cyclic-subsetprovedall subs proved validrefs-null-02, validrefs-subset, cyclic-def-simple,
cyclic-oneprovedall subs proved validrefs-one, validrefs-class, cyclic-def-simple,
cyclic-deleteprovedall subs proved validrefs-delete, validrefs-delete-02, cyclic-def-simple,
cyclic-classprovedall subs proved validrefs-superclass, validrefs-class, cyclic-def-simple,
cyclic-arrayprovedall subs proved validrefs-superclass, validrefs-array, cyclic-def-simple,
cyclic-addarray-this-01provedall subs proved validrefs-sametype, validrefs-superset-junkref, validrefs-addarray, validrefs-array, validrefs-is-junk, cyclic-def-simple,
cyclic-addarray-thisprovedall subs proved validrefs-null-02, validrefs-array, validrefs-is-junk, cyclic-def-simple,
cyclic-addarray-otherprovedall subs proved validrefs-addarray-junkref, validrefs-addarray, cyclic-def-simple,
cyclic-addarray-noreftypeprovedall subs proved validrefs-array, validrefs-is-junk, validrefs-null, cyclic-def-simple,
validrefs-primtype-02provedall subs proved validrefs-primtype,
validrefs-delcycleprovedall subs proved validrefs-array, validrefs-class, validrefs-null, validrefs-superclass, validrefs-null-02, validrefs-is-junk, validrefs-postfix,
validrefs-primtype-01provedall subs proved validrefs-primtype,
validrefs-append-01provedall subs proved validrefs-append,
validrefs-subset-notnewprovedall subs proved validref-refs-last-valid-subset,
validrefs-transprovedall subs proved validrefs-trans-01,
validrefs-subset-equivprovedall subs proved validrefs-subset-01, validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null-02,
pathex-subsetprovedall subs proved validrefs-subset-01, pathex-def,
pathex-not-is-validref-02provedall subs proved validrefs-not, pathex-def,
pathex-validrefs-inprovedall subs proved validrefs-null-02, validrefs-is-junk, validrefs-superclass, validrefs-prefix, pathex-def,
validrefs-not-in-01provedall subs proved validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-not,
pathex-levelsubsetprovedall subs proved validrefs-levelsubset, pathex-def,
validrefs-delcycle-01provedall subs proved validrefs-array, validrefs-class, validrefs-superclass, validrefs-null-02, validrefs-is-junk, validrefs-postfix,
pathex-def-simpleprovedall subs proved validrefs-not, validrefs-null-02, validrefs-is-junk, validrefs-superclass, validrefs-sametype, pathex-def,
validrefs-addobj-01provedall subs proved validrefs-primtype, validrefs-type, validrefs-null-02, validrefs-is-junk, validrefs-addobj-new, validrefs-class,
pathexplus-pathexprovedall subs proved validrefs-prefix, validrefs-array, validrefs-class, step-exists-def, validrefs-postfix, validrefs-not, validrefs-null-02, validrefs-is-junk, pathex-def, pathex-plus-def,
pathex-oneprovedall subs proved validrefs-one, validrefs-null-01, validrefs-not, pathex-def,
validrefs-deleteprovedall subs proved validrefs-null-01, validrefs-array, validrefs-class, validrefs-delete-02, validrefs-is-junk, validrefs-null, validrefs-empty,
validrefs-superset-junkrefprovedall subs proved validrefs-newref, validrefs-subset,
cyclic-def-simpleprovedall subs proved validrefs-array, validrefs-is-junk, validrefs-null, cyclic-def, cyclic-def-object,
validrefs-maxlenprovedall subs proved validrefs-array, validrefs-delete-03, validrefs-class, validrefs-is-junk, validrefs-null,
validrefs-primtype-03provedall subs proved validrefs-primtype,
validrefs-put-notin-01provedall subs proved validrefs-null-02, validrefs-not, validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-one,
validrefs-put-notin-03provedall subs proved validrefs-not, validrefs-array, validrefs-put-notin, validrefs-class, validrefs-null-02, validrefs-is-junk,
validrefs-voidprovedall subs proved validrefs-primtype, validrefs-null-01, validrefs-empty,
validrefs-addobj-junkrefprovedall subs proved validrefs-array, validrefs-null-02, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-empty,
validrefs-addarrayprovedall subs proved validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk, validrefs-empty,
validrefs-addarray-junkrefprovedall subs proved validrefs-array, validrefs-null-02, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-empty,
cyclic-def-objectprovedall subs proved validrefs-class, validrefs-is-junk, validrefs-null, validrefs-sametype, cyclic-def,
validrefs-put-badarrayfield-01provedall subs proved validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null-02,
validrefs-put-badarrayfieldprovedall subs proved validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk,
validrefs-put-badclassfield-01provedall subs proved validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk,
validrefs-put-badclassfieldprovedall subs proved validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk, validrefs-null-01, validrefs-one, validrefs-empty,
validrefs-del-junkrefsprovedall subs proved validrefs-array, validrefs-one, validrefs-null-01, validrefs-class, validrefs-null,
validrefs-subtypeprovedall subs proved validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk,
validrefs-junkrefs-appendprovedall subs proved validrefs-array, validrefs-class, validrefs-null-02,
validrefs-levelsubsetprovedall subs proved validrefs-class, validrefs-array, validrefs-null-02, validrefs-is-junk, validrefs-empty,
validrefs-levelsubset-01provedall subs proved validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk, validrefs-empty,
validrefs-put-array-badindexprovedall subs proved validrefs-array, validrefs-class, validrefs-null-01, validrefs-null-02, validrefs-is-junk, validrefs-empty,
validrefs-put-notin-02provedall subs proved validrefs-null-02, validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-one,
validrefs-put-lastprovedall subs proved validrefs-array, validrefs-null-01, validrefs-one, validrefs-class, validrefs-null-02, validrefs-is-junk,
pathex-nullprovedall subs proved validrefs-null-02, pathex-def,
validrefs-sametype-03provedall subs proved validrefs-sametype,
validrefs-putbyteprovedall subs proved validrefs-one, validrefs-class, validrefs-array, validrefs-null-02, validrefs-is-junk, validrefs-empty,
validrefs-put-statfieldprovedall subs proved validrefs-null-01, validrefs-null-02, validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-empty,
validrefs-typeprovedall subs proved validrefs-one, validrefs-class, validrefs-array, validrefs-null-02, validrefs-is-junk,
validrefs-addobj-newprovedall subs proved validrefs-newref, validrefs-addobj-notin,
validrefs-appendprovedall subs proved validrefs-array, validrefs-class, validrefs-is-junk, validrefs-sametype, validrefs-superclass, validrefs-null-02, validrefs-one,
validrefs-postfixprovedall subs proved validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk, validrefs-sametype,
validrefs-delete-02provedall subs proved validrefs-null-02, validrefs-is-junk, validrefs-null-01,
validrefs-delete-03provedall subs proved validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk, validrefs-empty,
validrefs-contains-nullprovedall subs proved validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-null-01, validrefs-null-02,
validrefs-prefixprovedall subs proved validrefs-null-02, validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-empty,
validrefs-notprovedall subs proved validrefs-null-02, validrefs-is-junk, validrefs-null-01,
validrefs-put-notinprovedall subs proved validrefs-null-02, validrefs-null-01, validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-empty,
validrefs-subset-01provedall subs proved validrefs-null-01, validrefs-array, validrefs-null-02, validrefs-class, validrefs-is-junk, validrefs-null,
validref-refs-last-valid-subsetprovedall subs proved validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk,
validrefs-subsetprovedall subs proved validrefs-null-01, validrefs-array, validrefs-null-02, validrefs-class, validrefs-is-junk, validrefs-null,
validrefs-trans-01provedall subs proved validrefs-array, validrefs-class, validrefs-is-junk, validrefs-superclass, validrefs-null-02, validrefs-one, validrefs-sametype, validrefs-empty,
validrefs-primtypeprovedall subs proved validrefs-null-02, validrefs-is-junk, validrefs-null-01, validrefs-empty,
validrefs-sametype-02provedall subs proved validrefs-sametype,
validrefs-sametype-01provedall subs proved validrefs-sametype,
validrefs-primarrayprovedall subs proved validrefs-array, validrefs-null, validrefs-null-01, validrefs-null-02, validrefs-is-junk, validrefs-empty,
validrefs-objectprovedall subs proved validrefs-sametype,
validrefs-lastelemprovedall subs proved validrefs-one, validrefs-array, validrefs-null-02, validrefs-empty, validrefs-class, validrefs-is-junk, validrefs-null,
validrefs-junkrefs-01provedall subs proved validrefs-array, validrefs-class, validrefs-one, validrefs-empty,
validrefs-junkrefsprovedall subs proved validrefs-array, validrefs-class, validrefs-one, validrefs-empty,
validrefs-has-nullprovedall subs proved validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-null-02,
validrefs-all-sameprovedall subs proved validrefs-array, validrefs-class, validrefs-null-02, validrefs-is-junk, validrefs-empty,
validrefs-delprovedall subs proved validrefs-newref,
validrefs-superclassprovedall subs proved validrefs-null-01, validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-empty,
validrefs-addobj-notinprovedall subs proved validrefs-null-01, validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-empty,
validrefs-addobjprovedall subs proved validrefs-null-01, validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-empty,
validrefs-oneprovedall subs proved validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null-01,
validrefs-sametypeprovedall subs proved validrefs-null-01, validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null,
validrefs-null-02provedall subs proved validrefs-null, validrefs-null-01,
validrefs-not-typeexprovedall subs proved validrefs-not-in,
validrefs-set-nullprovedall subs proved validrefs-array, validrefs-null-01, validrefs-class, validrefs-is-junk, validrefs-null,
validrefs-not-inprovedall subs proved validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null,
validrefs-newrefprovedall subs proved validrefs-array, validrefs-class, validrefs-is-junk, validrefs-null, validrefs-empty,
validrefs-null-01provedall subs proved validrefs-null,
okbar-nopathprovedall subs proved validrefs-array, pathex-def,
pathex-defaxiom
pathex-plus-defaxiom
step-exists-defaxiom
validrefs-emptyaxiom
cyclic-defaxiom
validrefs-classaxiom
validrefs-nullaxiom
validrefs-is-junkaxiom
validrefs-arrayaxiom