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Proof step 168 from proof addarray-disjoint-nosharing-01 (previous step)

sks = sk + sks1, (addarray(r, ty, vals, st)[r -- sks]) = refval(r0), (addarray(r, ty, vals, st)[r -- sks0]) = refval(r0), 0 ≤ sk .index, 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) ⊦ sks = [], r = jvmref, r0 = jvmref, sks0 = [], sks0 = sks, vals = [], dups(vals .nonnullrefs), hasSharing(vals .nonnullrefs, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 167:
(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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : int-abs, , forward-le-01, ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, e-01, ⊦ sk ' + sks ≠ []], [CSIMPNAMEDSEQ : list, storekeys, c, ⊦ sk + sks = sk ' + sks])]]