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Proof step 155 from proof addarray-disjoint-nosharing-01 (previous step)

(addarray(r, ty, vals, st)[r -- (i0 ' ' + sks)]) = refval(r0), (addarray(r, ty, vals, st)[r -- (i ' ' + sks1)]) = refval(r0), vals[i→n(i)] = refval(r1), vals[i→n(i0)] = refval(r2), 0 ≤ i0, fits(r2, sks, addarray(r, ty, vals, st)), fits(r1, sks1, addarray(r, ty, vals, st)), 0 ≤ i, i0 < n→i(# vals), disjoint(str, vals .nonnullrefs, st), validreflist(str, vals, ty, st), newref(r, st), i < n→i(# vals) ⊦ i0 ' ' + sks = i ' ' + sks1, r = jvmref, vals = [], r0 = jvmref, dups(vals .nonnullrefs), hasSharing(vals .nonnullrefs, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ is_referencevalue(st[r -- sks]) ∧ sks ≠ [] → st[r -- sks] = st[st[r -- sks .first] .refval -- sks .rest]
Proof step 154:
is_referencevalue(addarray(r, ty, vals, st)[r -- (i0 ' ' + sks)]) ∧ i0 ' ' + sks ≠ [], (addarray(r, ty, vals, st)[(addarray(r, ty, vals, st)[r -- (i0 ' ' + sks) .first]) .refval -- (i0 ' ' + sks) .rest]) = refval(r0), (addarray(r, ty, vals, st)[r -- (i ' ' + sks1)]) = refval(r0), vals[i→n(i)] = refval(r1), vals[i→n(i0)] = refval(r2), 0 ≤ i0, fits(r2, sks, addarray(r, ty, vals, st)), fits(r1, sks1, addarray(r, ty, vals, st)), 0 ≤ i, i0 < n→i(# vals), disjoint(str, vals .nonnullrefs, st), validreflist(str, vals, ty, st), newref(r, st), i < n→i(# vals) ⊦ i0 ' ' + sks = i ' ' + sks1, r = jvmref, vals = [], r0 = jvmref, dups(vals .nonnullrefs), hasSharing(vals .nonnullrefs, 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] → [i0 ' ' + sks, r, addarray(r, ty, vals, st)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0, 1, 0)) 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], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))])], [EXTRATERMS : (i0 ' ' + sks, r, addarray(r, ty, vals, st))]]