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Proof step 663 from proof hasSharing-put-index-refval (previous step)

¬ ( ¬ (∃ sks0, sks1. sks2 = sks0 + (i ' + sks1) ∧ st[r2 -- sks0] .refval = r0 ∧ (∀ sks2. sks2 + i ' ⊑ sks0 → st[r2 -- sks2] .refval ≠ r0)) ∧ i ' ≠ _type ∧ i ' ≠ _length), st[r0 -- sks] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r2 -- sks2]) = refval(r1), 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 ⊦ i ' ' + sks2 = sks, r0 = jvmref, r0 = r2, r1 = jvmref, sks = [], sks2 = [], r2 = jvmref, 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 662:
(st[st[r2 -- sks0] .refval -- i ', refval(r2)][r2 -- (sks0 + i ' ' + sks1)]) = refval(r1), st[st[r2 -- sks0] .refval -- _type] .type = mkarraytype(ty), st[st[r2 -- sks0] .refval -- sks] = refval(r1), 0 ≤ i, i < st[st[r2 -- sks0] .refval -- _length] .intval, validref(str, r2, ty, st), disjoint(str, st[r2 -- sks0] .refval ' + r2 ', st), fits(st[r2 -- sks0] .refval, sks, st), fits(r2, sks0 + i ' ' + sks1, st[st[r2 -- sks0] .refval -- i ', refval(r2)]), 0 < st[st[r2 -- sks0] .refval -- _length] .intval ⊦ r2 = jvmref, sks = [], r1 = jvmref, st[r2 -- sks0] .refval = r2, st[r2 -- sks0] .refval = jvmref, i ' ' + sks0 + i ' ' + sks1 = sks, hasSharing(st[r2 -- sks0] .refval, st), hasSharing(r2, st), junkref(str, st[r2 -- sks0] .refval, st), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks0 → st[r2 -- sks3] .refval ≠ st[r2 -- sks0] .refval), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[st[r2 -- sks0] .refval -- sks1] .refval = st[r2 -- sks0] .refval ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[st[r2 -- sks0] .refval -- sks2] .refval ≠ st[st[r2 -- sks0] .refval -- sks1] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : int-abs, , forward-le-05, ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, e-03, ⊦ sks + sk ' + sks0 ≠ []], [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])]]