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Proof step 691 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[r -- sks] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][(st[r0 -- i ', refval(r2)][r -- sks1]) .refval -- (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, sks1 = [], 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 690:
st[r -- sks] = refval(r1), st[st[r -- sks3] .refval -- _type] .type = mkarraytype(ty), (st[st[r -- sks3] .refval -- i ', refval(r2)][(st[st[r -- sks3] .refval -- i ', refval(r2)][r -- (sks3 + i ' ' + sks0)]) .refval -- (i ' ' + sks2)]) = refval(r1), st[r -- (sks3 + i ' ' + sks0)] = refval(st[r -- sks3] .refval), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[st[r -- sks3] .refval -- _length] .intval, 0 ≤ i, fits(r2, sks2, st[st[r -- sks3] .refval -- i ', refval(r2)]), fits(r, sks3 + i ' ' + sks0, st), 0 < st[st[r -- sks3] .refval -- _length] .intval, r2 = jvmref → is_reftype(ty), ∀ sks1. sks1 + i ' ' ⊑ sks3 → st[r -- sks1] .refval ≠ st[r -- sks3] .refval ⊦ st[r -- sks3] .refval = jvmref, r = r2, r1 = jvmref, sks = [], sks3 + (i ' ' + sks0) + i ' ' + sks2 = sks, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks0, sks1. sks = sks0 + i ' ' + sks1 ∧ st[r -- sks0] .refval = st[r -- sks3] .refval ∧ (∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r -- sks2] .refval ≠ st[r -- sks0] .refval), ∃ sks1, sks5. sks3 + i ' ' + sks0 = sks1 + i ' ' + sks5 ∧ st[r -- sks1] .refval = st[r -- sks3] .refval ∧ (∀ sks4. sks4 + i ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ st[r -- sks1] .refval), ∃ sks1. ¬ (sks1 + i ' ' ⊑ sks3 + i ' ' + sks0 → st[r -- sks1] .refval ≠ st[r -- sks3] .refval)

Rule argument

[emptyarg]

Additional information

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