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Proof step 73 from proof hasSharing-put-index-refval (previous step)

¬ (sks ≠ [] ∧ i ' ' + sks1 ≠ []), (st[r0 -- i ', refval(r1)][r0 -- sks]) = refval(r), st[r0 -- sks] = refval(r0), (st[r0 -- i ', refval(r1)][r0 -- (sks + i ' ' + sks1)]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r1)][r -- i ']) = refval(r2), fits(r2, sks1, st[r0 -- i ', refval(r1)]), fits(r0, sks, st), validref(str, r1, ty, st), disjoint(str, r0 ' + r1 ', st), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, is_arraytype(st[r -- _type] .type) → i < st[r -- _length] .intval ⊦ r = jvmref, r1 = jvmref, r0 = r1, r0 = jvmref, sks + i ' ' + sks1 = i ' ', is_classtype(st[r -- _type] .type), hasSharing(r0, st), hasSharing(r1, st), junkref(str, r0, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r0 -- sks2] .refval ≠ r0), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r0 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r0 -- sks2] .refval ≠ r0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
⊦ fits(r, [], st)
Proof step 72:
st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r -- (i ' ' + sks1)]) = refval(r2), 0 < st[r -- _length] .intval, i < st[r -- _length] .intval, 0 ≤ i, disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), fits(r2, sks1, st[r -- i ', refval(r2)]) ⊦ r = jvmref, r = r2, r2 = jvmref, sks1 = [], junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javatype, , test-16, ⊦ ¬ is_classtype (mkarraytype(ty))], [CSIMPNAMEDFORWARD : int-abs, , forward-le-05, ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPNAMEDSEQ : store, javastore, At-same, ⊦ (st[rk, val][rk]) = val], [CSIMPNAMEDSEQ : list, storekeys, e-02, ⊦ sks + sk ' ≠ []], [CSIMPNAMEDSEQ : list-last, storekeys, eq-01-01, ⊦ sks ⊑ [] ↔ sks = []], [CSIMPNAMEDSEQ : list, storekeys, e-03, ⊦ sks + sk ' + sks0 ≠ []], [CSIMPNAMEDSEQ : list, storekeys, app-04, ⊦ sks = sks + sks0 ↔ sks0 = []], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPNAMEDSEQ : storefuns, , lookup-empty, ⊦ st[r -- []] = refval(r)], [CSIMPNAMEDSEQ : list, storekeys, Nil, ⊦ [] + sks = sks], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, e, ⊦ sk ' ≠ []], [CSIMPNAMEDSEQ : list, storekeys, app-02-ant, ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []])]]