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Proof step 120 from proof hasSharing-put-index-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 119:
st[r0 -- sks0] .refval = r0, (st[r0 -- i ', refval(r4)][r0 -- (sks0 + i ' ' + sks4)]) = refval(r), st[r0 -- (sks0 + i ' ' + sks4)] = refval(r0), (st[r0 -- i ', refval(r4)][r4 -- sks3]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r0 -- ((sks0 + i ' ' + sks4) + i ' ' + sks1)]) = refval(r1), fits(r4, sks3, st[r0 -- i ', refval(r4)]), disjoint(str, r0 ' + r4 ', st), validref(str, r4, ty, st), fits(r, i ' ' + sks1, st[r0 -- i ', refval(r4)]), fits(r0, sks0 + i ' ' + sks4, st[r0 -- i ', refval(r4)]), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval ⊦ r4 = jvmref, sks3 = [], (sks0 + i ' ' + sks4) + i ' ' + sks1 = i ' ' + sks3, r0 = jvmref, r0 = r4, r1 = jvmref, junkref(str, r0, st), hasSharing(r4, st), hasSharing(r0, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks0 → st[r0 -- sks2] .refval ≠ r0), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks0 + i ' ' + sks4 → st[r0 -- sks2] .refval ≠ r0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : specialkeys, , len, ⊦ _length ≠ i '], [CSIMPNAMEDSEQ : specialkeys, , type-03, ⊦ _type ≠ i '], [CSIMPNAMEDSEQ : list, storekeys, Last, ⊦ sks + sk = sks + sk '], [CSIMPNAMEDSEQ : list, storekeys, c, ⊦ sk + sks = sk ' + sks])]]