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Proof step 82 from proof hasSharing-addobj-same (previous step)

sk ∈ fis, (addobj(r, class, fis, st)[fis[sk] .refval -- sks1]) = refval(r0), fis .keys = instfields(class), (addobj(r, class, fis, st)[r -- sks0]) = refval(r0), validfieldinits(str, fis, st), newref(r, st), fits(r, sks0, addobj(r, class, fis, st)), fits(r, sk ' + sks1, addobj(r, class, fis, st)), disjoint(str, fis .vals .nonnullrefs, st), is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks1)]) ⊦ r = jvmref, r0 = jvmref, sks0 = [], sks0 = sk ' + sks1, junkref(str, r, addobj(r, class, fis, st)), hasSharing(fis .vals .nonnullrefs, st), dups(fis .vals .nonnullrefs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ sks ≠ [] → ( fits(r, sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sks .first]) ∧ (is_classtype(st[r -- _type] .type) → sks .first ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sks .first) ∧ 0 ≤ sks .first .index ∧ sks .first .index < st[r -- _length] .intval) ∧ fits(st[r -- sks .first] .refval, sks .rest, st))
Proof step 81:
sk ' + sks1 ≠ [], sk ∈ fis, (addobj(r, class, fis, st)[fis[sk] .refval -- sks1]) = refval(r0), fis .keys = instfields(class), (addobj(r, class, fis, st)[r -- sks0]) = refval(r0), validfieldinits(str, fis, st), newref(r, st), fits(r, sks0, addobj(r, class, fis, st)), r ≠ jvmref ∧ is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks1) .first]) ∧ ( is_classtype((addobj(r, class, fis, st)[r -- _type]) .type) → (sk ' + sks1) .first ∈ instfields((addobj(r, class, fis, st)[r -- _type]) .type .class)) ∧ ( is_arraytype((addobj(r, class, fis, st)[r -- _type]) .type) → is_indexkey((sk ' + sks1) .first) ∧ 0 ≤ (sk ' + sks1) .first .index ∧ (sk ' + sks1) .first .index < (addobj(r, class, fis, st)[r -- _length]) .intval) ∧ fits((addobj(r, class, fis, st)[r -- (sk ' + sks1) .first]) .refval, (sk ' + sks1) .rest, addobj(r, class, fis, st)), disjoint(str, fis .vals .nonnullrefs, st), is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks1)]) ⊦ r = jvmref, r0 = jvmref, sks0 = [], sks0 = sk ' + sks1, junkref(str, r, addobj(r, class, fis, st)), hasSharing(fis .vals .nonnullrefs, st), dups(fis .vals .nonnullrefs)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-rec antecedent: succedent: sks ≠ [] → ( fits(r, sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sks .first]) ∧ ( is_classtype(st[r -- _type] .type) → sks .first ∈ instfields(st[r -- _type] .type .class)) ∧ ( is_arraytype(st[r -- _type] .type) → is_indexkey(sks .first) ∧ 0 ≤ sks .first .index ∧ sks .first .index < st[r -- _length] .intval) ∧ fits(st[r -- sks .first] .refval, sks .rest, st)) substlist: [st, sks, r] → [addobj(r, class, fis, st), sk ' + sks1, r] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 7)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, storekeys, app-02-ant, ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPNAMEDSEQ : list, storekeys, e, ⊦ sk ' ≠ []], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])], [EXTRATERMS : (addobj(r, class, fis, st), sk ' + sks1, r)]]