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Proof step 167 from proof addarray-disjoint-nosharing-01 (previous step)

(addarray(r, ty, vals, st)[r -- sks0]) = refval(r0), (addarray(r, ty, vals, st)[r -- (sk ' + sks1)]) = refval(r0), sk .index < n→i(# vals), is_indexkey(sk), fits(r, sks0, addarray(r, ty, vals, st)), fits((addarray(r, ty, vals, st)[r -- sk]) .refval, sks1, addarray(r, ty, vals, st)), is_referencevalue(addarray(r, ty, vals, st)[r -- sk]), disjoint(str, vals .nonnullrefs, st), validreflist(str, vals, ty, st), newref(r, st), 0 ≤ sk .index ⊦ vals = [], r = jvmref, r0 = jvmref, sks0 = [], sks0 = sk ' + sks1, dups(vals .nonnullrefs), hasSharing(vals .nonnullrefs, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 166:
sk = i ', (addarray(r, ty, vals, st)[r -- sks0]) = refval(r0), (addarray(r, ty, vals, st)[r -- (sk ' + sks1)]) = refval(r0), i < n→i(# vals), is_indexkey(sk), fits(r, sks0, addarray(r, ty, vals, st)), fits((addarray(r, ty, vals, st)[r -- sk]) .refval, sks1, addarray(r, ty, vals, st)), is_referencevalue(addarray(r, ty, vals, st)[r -- sk]), disjoint(str, vals .nonnullrefs, st), validreflist(str, vals, ty, st), newref(r, st), 0 ≤ i ⊦ vals = [], r = jvmref, r0 = jvmref, sks0 = [], sks0 = sk ' + sks1, dups(vals .nonnullrefs), hasSharing(vals .nonnullrefs, st)

Rule argument

[x0lemmaarg: spec-name: storekey instance-name: lemma-name: elim-04 antecedent: succedent: is_indexkey(sk) → (i = sk .index ↔ sk = i ') substlist: [sk, i] → [sk, i] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_indexkey(sk) → (i = sk .index ↔ sk = i ')])], [EXTRATERMS : (sk, i)]]