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Proof step 86 from proof addarray-disjoint-nosharing (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ is_referencevalue(st[r -- sks]) ∧ sks ≠ [] → st[r -- sks] = st[st[r -- sks .first] .refval -- sks .rest]
Proof step 85:
is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks)]) ∧ i0 ' ' + sks ≠ [], (addarray(r, ty, mkjavavalues(refs), st)[(addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks) .first]) .refval -- (i0 ' ' + sks) .rest]) = refval(r0), (addarray(r, ty, mkjavavalues(refs), st)[r -- (i ' ' + sks1)]) = refval(r0), i→n(i) < # refs, 0 ≤ i0, fits(refs[i→n(i0)], sks, addarray(r, ty, mkjavavalues(refs), st)), fits(refs[i→n(i)], sks1, addarray(r, ty, mkjavavalues(refs), st)), disjoint(str, refs, st), validreflist(str, mkjavavalues(refs), ty, st), newref(r, st), 0 ≤ i, i < n→i(# refs), i0 < n→i(# refs), i→n(i0) < # refs ⊦ i0 ' ' + sks = i ' ' + sks1, r = jvmref, refs = [], r0 = jvmref, dups(refs), hasSharing(refs, 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, mkjavavalues(refs), 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 : ([CSIMPSEQ : ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPSEQ : ⊦ sk ' ≠ []], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])], [EXTRATERMS : (i0 ' ' + sks, r, addarray(r, ty, mkjavavalues(refs), st))]]