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Proof step 554 from proof hasSharing-put-index-refval (previous step)

¬ (∃ sks0, sks2. sks1 = sks0 + (i ' + sks2) ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r -- sks2] .refval ≠ r0)), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r -- sks0]) = refval(r1), (st[r0 -- i ', refval(r2)][r3 -- i ']) = refval(r4), st[r -- sks1] = refval(r3), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r2)][r4 -- sks3]) = refval(r1), fits(r4, sks3, st[r0 -- i ', refval(r2)]), fits(r, sks1, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), fits(r, sks0, st[r0 -- i ', refval(r2)]), is_referencevalue(st[r0 -- i ', refval(r2)][r3 -- (i ' ' + sks3)]), is_arraytype(st[r3 -- _type] .type) → 0 ≤ i ∧ i < st[r3 -- _length] .intval, r2 = jvmref → is_reftype(ty) ⊦ r3 = jvmref, r0 = jvmref, r = r2, r1 = jvmref, sks0 = [], sks0 = sks1 + i ' ' + sks3, sks1 = [], is_classtype(st[r3 -- _type] .type), junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks, sks2. sks1 = sks + i ' ' + sks2 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 553:
(st[r3 -- i ', refval(r4)][r -- sks0]) = refval(r1), st[r3 -- _type] .type = mkarraytype(ty), (st[r3 -- i ', refval(r4)][r4 -- sks3]) = refval(r1), st[r -- sks1] = refval(r3), is_referencevalue(st[r3 -- i ', refval(r4)][r3 -- (i ' ' + sks3)]), fits(r, sks0, st[r3 -- i ', refval(r4)]), validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks1, st), fits(r4, sks3, st[r3 -- i ', refval(r4)]), i < st[r3 -- _length] .intval, 0 ≤ i, 0 < st[r3 -- _length] .intval, r4 = jvmref → is_reftype(ty) ⊦ sks1 = [], sks0 = sks1 + i ' ' + sks3, sks0 = [], r1 = jvmref, r = r4, r3 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r3), ∃ sks, sks2. sks1 = sks + i ' ' + sks2 ∧ st[r -- sks] .refval = r3 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : int-abs, , forward-le-01, ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPNAMEDFORWARD : int-abs, , forward-le-05, ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPNAMEDSEQ : javatype, , test-09, ⊦ is_arraytype(mkarraytype(ty))], [CSIMPNAMEDSEQ : javatype, , test-16, ⊦ ¬ is_classtype (mkarraytype(ty))], [CSIMPNAMEDSEQ : store, javastore, At-same, ⊦ (st[rk, val][rk]) = val], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPNAMEDSEQ : list, storekeys, Last, ⊦ sks + sk = sks + sk '], [CSIMPNAMEDSEQ : list, storekeys, c, ⊦ sk + sks = sk ' + sks])]]