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Proof step 277 from proof hasSharing-put-index-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 276:
st[r -- sks0] = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r4)][r4 -- (sks + i ' ' + sks1)]) = refval(r1), st[r4 -- sks] = refval(r), (st[r -- i ', refval(r4)][r4 -- sks]) = refval(r0), 0 < st[r -- _length] .intval, 0 ≤ i, i < st[r -- _length] .intval, fits(r, sks0, st), validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r4, sks, st), fits(r0, i ' ' + sks1, st[r -- i ', refval(r4)]) ⊦ sks0 = [], r1 = jvmref, r = r4, r = jvmref, sks0 = i ' ' + sks + i ' ' + sks1, r4 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), ∃ sks2, sks1. sks0 = sks2 + i ' ' + sks1 ∧ st[r -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r -- sks3] .refval ≠ r), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r4 -- sks2] .refval ≠ r), ∃ sks3, sks4. sks = sks3 + i ' ' + sks4 ∧ st[r4 -- sks3] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks3 → st[r4 -- sks2] .refval ≠ st[r4 -- sks3] .refval)

Rule argument

[emptyarg]

Additional information

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