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Proof step 71 from proof hasSharing-addobj-same (previous step)

sk0 ' + sks ≠ [], fis[sk] = refval(r1), (addobj(r, class, fis, st)[r1 -- sks1]) = refval(r0), fis .keys = instfields(class), (addobj(r, class, fis, st)[(addobj(r, class, fis, st)[r -- sk0]) .refval -- sks]) = refval(r0), sk ∈ fis, validfieldinits(str, fis, st), newref(r, st), r ≠ jvmref ∧ is_referencevalue(addobj(r, class, fis, st)[r -- (sk0 ' + sks) .first]) ∧ ( is_classtype((addobj(r, class, fis, st)[r -- _type]) .type) → (sk0 ' + sks) .first ∈ instfields((addobj(r, class, fis, st)[r -- _type]) .type .class)) ∧ ( is_arraytype((addobj(r, class, fis, st)[r -- _type]) .type) → is_indexkey((sk0 ' + sks) .first) ∧ 0 ≤ (sk0 ' + sks) .first .index ∧ (sk0 ' + sks) .first .index < (addobj(r, class, fis, st)[r -- _length]) .intval) ∧ fits((addobj(r, class, fis, st)[r -- (sk0 ' + sks) .first]) .refval, (sk0 ' + sks) .rest, addobj(r, class, fis, st)), fits(r1, sks1, addobj(r, class, fis, st)), sk ∈ instfields(class), is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks1)]), disjoint(str, fis .vals .nonnullrefs, st), is_referencevalue(addobj(r, class, fis, st)[r -- (sk0 ' + sks)]) ⊦ r = jvmref, r0 = jvmref, sk0 ' + sks = sk ' + sks1, junkref(str, r, addobj(r, class, fis, st)), hasSharing(fis .vals .nonnullrefs, st), dups(fis .vals .nonnullrefs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
fis[sk] = refval(r1), (addobj(r, class, fis, st)[r1 -- sks1]) = refval(r0), fis .keys = instfields(class), (addobj(r, class, fis, st)[(addobj(r, class, fis, st)[r -- sk0]) .refval -- sks]) = refval(r0), fits(r1, sks1, addobj(r, class, fis, st)), sk ∈ instfields(class), is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks1)]), disjoint(str, fis .vals .nonnullrefs, st), is_referencevalue(addobj(r, class, fis, st)[r -- (sk0 ' + sks)]), sk ∈ fis, validfieldinits(str, fis, st), newref(r, st), is_referencevalue(addobj(r, class, fis, st)[r -- sk0]), fits((addobj(r, class, fis, st)[r -- sk0]) .refval, sks, addobj(r, class, fis, st)), sk0 ∈ instfields(class) ⊦ r0 = jvmref, sk0 ' + sks = sk ' + sks1, r = jvmref, junkref(str, r, addobj(r, class, fis, st)), hasSharing(fis .vals .nonnullrefs, st), dups(fis .vals .nonnullrefs)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javatype, , test-28, ⊦ ¬ is_arraytype (mkclasstype(class))], [CSIMPNAMEDSEQ : javatype, , sel-02, ⊦ mkclasstype(class) .class = class], [CSIMPNAMEDSEQ : javatype, , test-10, ⊦ is_classtype (mkclasstype(class))], [CSIMPNAMEDSEQ : javavalue, , sel-11, ⊦ typeval(ty) .type = ty], [CSIMPNAMEDSEQ : addfuns, , add-type, ¬ _type ∈ fis ⊦ (addobj(r, class1, fis, st) [r -- _type ] ) = typeval(mkclasstype(class1))], [CSIMPNAMEDSEQ : addfuns, , instfields-type, ⊦ fis .keys = instfields(class) → ¬ _type ∈ fis], [CSIMPNAMEDSEQ : list, storekeys, c-07, ⊦ (sk ' + sks) .rest = sks], [CSIMPNAMEDSEQ : list, storekeys, c-08, ⊦ (sk ' + sks) .first = sk], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, e-01, ⊦ sk ' + sks ≠ []])]]