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Proof step 162 from proof addarray-disjoint-nosharing-01 (previous step)

sks0 ≠ [], (addarray(r, ty, vals, st)[r -- (i ' ' + sks1)]) = refval(r0), (addarray(r, ty, vals, st)[r -- sks0]) = refval(r0), vals[i→n(i)] = refval(r1), 0 ≤ i, fits(r1, sks1, addarray(r, ty, vals, st)), r ≠ jvmref ∧ is_referencevalue(addarray(r, ty, vals, st)[r -- sks0 .first]) ∧ (is_classtype((addarray(r, ty, vals, st)[r -- _type]) .type) → sks0 .first ∈ instfields((addarray(r, ty, vals, st)[r -- _type]) .type .class)) ∧ ( is_arraytype((addarray(r, ty, vals, st)[r -- _type]) .type) → is_indexkey(sks0 .first) ∧ 0 ≤ sks0 .first .index ∧ sks0 .first .index < (addarray(r, ty, vals, st)[r -- _length]) .intval) ∧ fits((addarray(r, ty, vals, st)[r -- sks0 .first]) .refval, sks0 .rest, addarray(r, ty, vals, st)), i < n→i(# vals), newref(r, st), validreflist(str, vals, ty, st), disjoint(str, vals .nonnullrefs, st) ⊦ sks0 = i ' ' + sks1, sks0 = [], r0 = jvmref, r = jvmref, vals = [], hasSharing(vals .nonnullrefs, st), dups(vals .nonnullrefs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 161:
(addarray(r, ty, vals, st)[r -- (i ' ' + sks1)]) = refval(r0), (addarray(r, ty, vals, st)[r -- sks0]) = refval(r0), vals[i→n(i)] = refval(r1), 0 ≤ i, fits(r1, sks1, addarray(r, ty, vals, st)), is_referencevalue(addarray(r, ty, vals, st)[r -- sks0 .first]), fits((addarray(r, ty, vals, st)[r -- sks0 .first]) .refval, sks0 .rest, addarray(r, ty, vals, st)), i < n→i(# vals), newref(r, st), validreflist(str, vals, ty, st), disjoint(str, vals .nonnullrefs, st), is_indexkey(sks0 .first), sks0 .first .index < n→i(# vals), 0 ≤ sks0 .first .index ⊦ sks0 = i ' ' + sks1, r0 = jvmref, vals = [], r = jvmref, sks0 = [], hasSharing(vals .nonnullrefs, st), dups(vals .nonnullrefs)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : int-abs, , forward-le-01, ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPNAMEDSEQ : javavalue, , sel-04, ⊦ intval(i) .intval = i], [CSIMPNAMEDSEQ : addarray, , length-1init-01, ⊦ (addarray(r, ty, vals, st) [r -- _length ] ) = intval(n→i(# vals))], [CSIMPNAMEDSEQ : javatype, , test-09, ⊦ is_arraytype(mkarraytype(ty))], [CSIMPNAMEDSEQ : javatype, , test-16, ⊦ ¬ is_classtype (mkarraytype(ty))], [CSIMPNAMEDSEQ : javavalue, , sel-11, ⊦ typeval(ty) .type = ty], [CSIMPNAMEDSEQ : addarray, , type-1init, ⊦ (addarray(r, ty, vals, st) [r -- _type ] ) = typeval(mkarraytype(ty))])]]