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Proof step 33 from proof addarray-disjoint-nosharing-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-in antecedent: succedent: sks ≠ [] ∧ ¬ junkref(str, r, st) ∧ fits(r, sks, st) → r -- sks ∈ st substlist: [sks, str, r, st] → [sks, str, r2, st] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 8)) 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 : addarray, , add-at-ok, ⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st) [r -- i ' ] ) = vals[i→n(i)]], [CSIMPNAMEDSEQ : storefuns, , instore-empty, ⊦ r -- [] ∈ st ↔ r ∈ st], [CSIMPNAMEDSEQ : junkrefs, , junkref-notin, ⊦ ¬ r ∈ st → ( junkref(str, r, st) ↔ r ≠ jvmref)])], [EXTRATERMS : (sks, str, r2, st)]]