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Proof step 78 from proof hasSharing-addobj-same (previous step)

(addobj(r, class, fis, st)[r -- sks0]) = refval(r0), fis .keys = instfields(class), (addobj(r, class, fis, st)[r1 -- sks1]) = refval(r0), fis[sk] = refval(r1), sk ∈ instfields(class), fits(r1, sks1, addobj(r, class, fis, st)), fits(r, sks0, addobj(r, class, fis, st)), newref(r, st), validfieldinits(str, fis, st), sk ∈ fis, is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks1)]), disjoint(str, fis .vals .nonnullrefs, st) ⊦ r = jvmref, sks0 = sk ' + sks1, sks0 = [], r0 = jvmref, dups(fis .vals .nonnullrefs), hasSharing(fis .vals .nonnullrefs, st), junkref(str, r, addobj(r, class, fis, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ is_referencevalue(st[r -- sks]) ∧ sks ≠ [] → st[r -- sks] = st[st[r -- sks .first] .refval -- sks .rest]
Proof step 77:
is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks1)]) ∧ sk ' + sks1 ≠ [], (addobj(r, class, fis, st)[r -- sks0]) = refval(r0), fis .keys = instfields(class), (addobj(r, class, fis, st)[r1 -- sks1]) = refval(r0), fis[sk] = refval(r1), sk ∈ instfields(class), fits(r1, sks1, addobj(r, class, fis, st)), fits(r, sks0, addobj(r, class, fis, st)), newref(r, st), validfieldinits(str, fis, st), sk ∈ fis, is_referencevalue(addobj(r, class, fis, st)[(addobj(r, class, fis, st)[r -- (sk ' + sks1) .first]) .refval -- (sk ' + sks1) .rest]), disjoint(str, fis .vals .nonnullrefs, st) ⊦ r = jvmref, sks0 = sk ' + sks1, sks0 = [], r0 = jvmref, dups(fis .vals .nonnullrefs), hasSharing(fis .vals .nonnullrefs, st), junkref(str, r, addobj(r, class, fis, st))

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: lookup-rec-refval antecedent: succedent: is_referencevalue(st[r -- sks]) ∧ sks ≠ [] → st[r -- sks] = st[st[r -- sks .first] .refval -- sks .rest] substlist: [sks, r, st] → [sk ' + sks1, r, addobj(r, class, fis, st)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 10)) 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 : (sk ' + sks1, r, addobj(r, class, fis, st))]]