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Proof step 686 from proof hasSharing-put-index-refval (previous step)

¬ (sks1 ≠ [] ∧ i ' ' + sks2 ≠ []), st[r -- sks] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r -- (sks1 + i ' ' + sks2)]) = refval(r1), st[r -- sks1] = refval(r0), fits(r2, sks2, st[r0 -- i ', refval(r2)]), fits(r, sks1, st), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r = r2, r1 = jvmref, sks = [], sks1 + i ' ' + sks2 = sks, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks0, sks3. sks1 = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 597:
⊦ fits(r, [], st)
Proof step 685:
(st[r0 -- i ', refval(r2)][r0 -- (i ' ' + sks2)]) = refval(r1), st[r0 -- sks] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), fits(r2, sks2, st[r0 -- i ', refval(r2)]), fits(r0, sks, st), disjoint(str, r0 ' + r2 ', st), validref(str, r2, ty, st), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, r2 = jvmref → is_reftype(ty) ⊦ i ' ' + sks2 = sks, r0 = jvmref, r0 = r2, r1 = jvmref, sks = [], junkref(str, r0, st), hasSharing(r2, st), hasSharing(r0, st), ∃ sks0, sks3. sks = sks0 + i ' ' + sks3 ∧ st[r0 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r0 -- sks2] .refval ≠ st[r0 -- sks0] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, storekeys, e-03, ⊦ sks + sk ' + sks0 ≠ []], [CSIMPNAMEDSEQ : list, storekeys, e-02, ⊦ sks + sk ' ≠ []], [CSIMPNAMEDSEQ : list-last, storekeys, eq-01-01, ⊦ sks ⊑ [] ↔ sks = []], [CSIMPNAMEDSEQ : list, storekeys, Nil, ⊦ [] + sks = sks], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPNAMEDSEQ : storefuns, , lookup-empty, ⊦ st[r -- []] = refval(r)], [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 = []])]]