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Proof step 224 from proof hasSharing-put-index-refval (previous step)

sks = [], (st[r0 -- i ', refval(r4)][r0 -- sks]) = refval(r), st[r0 -- sks] = refval(r0), (st[r0 -- i ', refval(r4)][r4 -- sks3]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r0 -- (sks + i ' ' + sks1)]) = refval(r1), (st[r0 -- i ', refval(r4)][r -- i ']) = refval(r2), fits(r2, sks1, st[r0 -- i ', refval(r4)]), fits(r0, sks, st), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, fits(r4, sks3, st[r0 -- i ', refval(r4)]), disjoint(str, r0 ' + r4 ', st), validref(str, r4, ty, st), is_arraytype(st[r -- _type] .type) → i < st[r -- _length] .intval ⊦ r = jvmref, r4 = jvmref, sks3 = [], sks + i ' ' + sks1 = i ' ' + sks3, r0 = jvmref, r0 = r4, r1 = jvmref, is_classtype(st[r -- _type] .type), junkref(str, r0, st), hasSharing(r4, st), hasSharing(r0, st), ∃ sks0, sks4. sks = sks0 + i ' ' + sks4 ∧ st[r0 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r0 -- sks2] .refval ≠ r0), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r0 -- sks2] .refval ≠ r0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 122:
⊦ fits(r, [], st)
Proof step 223:
(st[r -- i ', refval(r2)][r2 -- sks3]) = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r2)][r -- (i ' ' + sks1)]) = refval(r1), 0 < st[r -- _length] .intval, fits(r2, sks1, st[r -- i ', refval(r2)]), i < st[r -- _length] .intval, 0 ≤ i, fits(r2, sks3, st[r -- i ', refval(r2)]), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st) ⊦ r = jvmref, r = r2, r1 = jvmref, r2 = jvmref, sks3 = [], sks1 = sks3, 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-01, ⊦ sks + sks0 = sks + sks1 ↔ sks0 = sks1], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, Nil, ⊦ [] + sks = sks], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPNAMEDSEQ : storefuns, , lookup-empty, ⊦ st[r -- []] = refval(r)])]]