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Proof step 80 from proof addarray-disjoint-nosharing (previous step)

(addarray(r, ty, mkjavavalues(refs), st)[refs[i→n(i0)] -- sks]) = refval(r0), (addarray(r, ty, mkjavavalues(refs), st)[(addarray(r, ty, mkjavavalues(refs), st)[r -- i ']) .refval -- sks1]) = refval(r0), is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i ' ' + sks1)]), is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks)]), 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), i→n(i0) < # refs, i0 < n→i(# 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 17:
⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st)[r -- i ']) = vals[i→n(i)]
Proof step 79:
0 ≤ i ∧ i < n→i(# mkjavavalues(refs)), (addarray(r, ty, mkjavavalues(refs), st)[refs[i→n(i0)] -- sks]) = refval(r0), (addarray(r, ty, mkjavavalues(refs), st)[(mkjavavalues(refs)[i→n(i)]) .refval -- sks1]) = refval(r0), is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i ' ' + sks1)]), is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks)]), 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), i→n(i0) < # refs, i0 < n→i(# refs) ⊦ i0 ' ' + sks = i ' ' + sks1, r = jvmref, refs = [], r0 = jvmref, dups(refs), hasSharing(refs, st)

Rule argument

[x0lemmaarg: spec-name: addarray instance-name: lemma-name: add-at-ok antecedent: succedent: 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st)[r -- i ']) = vals[i→n(i)] substlist: [i, st, vals, ty, r] → [i, st, mkjavavalues(refs), ty, r] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ # mkjavavalues(refs) = # refs], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i→n(i) < n → ¬ n→i(n) ≤ i])], [EXTRATERMS : (i, st, mkjavavalues(refs), ty, r)]]