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Proof step 200 from proof hasSharing-addobj-same (previous step)

fis[sk] = refval(r0), st[r0 -- sks] = refval(r2), st[r3 -- sks0] = refval(r2), fis[sk0] = refval(r3), is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks)]), sk0 ∈ fis .keys, sk ∈ fis .keys, sk0 ∈ fis, sk ∈ fis, fits(r3, sks0, st), fits(r0, sks, st), newref(r, st), validfieldinits(str, fis, st) ⊦ r0 = jvmref, r = jvmref, r2 = jvmref, r3 = r0, r3 = jvmref, sk = sk0, refval(r2) = (addobj(r, class, fis, st)[r -- (sk0 ' + sks0)]), hasSharing(fis .vals .nonnullrefs, st), dups(fis .vals .nonnullrefs), junkref(str, r, addobj(r, class, fis, st)), junkref(str, r0, st), junkref(str, r3, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: lookup-rec-01 antecedent: succedent: sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks] substlist: [sks, sk, r, st] → [sks0, sk0, r, addobj(r, class, fis, st)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 6)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : storefuns, , lookup-empty, ⊦ st[r -- []] = refval(r)], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPNAMEDSEQ : list, storekeys, app, ⊦ sks + [] = sks], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : storefuns, , lookup-one, ⊦ st[r -- sk '] = st[r -- sk]], [CSIMPNAMEDSEQ : addfuns, , add-in-09, ⊦ sk ∈ fis → (addobj(r, class, fis, st) [r -- sk ] ) = fis[sk]])], [EXTRATERMS : (sks0, sk0, r, addobj(r, class, fis, st))]]