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Proof step 208 from proof hasSharing-put-index-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 207:
(st[r -- i ', refval(r2)][r2 -- (sks0 + i ' ' + sks)]) = refval(r1), st[r2 -- sks1] = refval(r1), st[r -- _type] .type = mkarraytype(ty), st[r2 -- sks0] = refval(r), 0 < st[r -- _length] .intval, fits(r2, sks0 + i ' ' + sks, st), 0 ≤ i, i < st[r -- _length] .intval, fits(r2, sks1, st), is_referencevalue(st[r -- i ', refval(r2)][r -- (i ' ' + sks1)]), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), ∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r2 -- sks2] .refval ≠ r ⊦ sks1 = sks0 + i ' ' + sks, r2 = jvmref, r1 = jvmref, r = r2, r = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks2, sks3. sks0 + i ' ' + sks = sks2 + i ' ' + sks3 ∧ st[r2 -- sks2] .refval = r ∧ (∀ sks. sks + i ' ' ⊑ sks2 → st[r2 -- sks] .refval ≠ st[r2 -- sks2] .refval), ∃ sks, sks2. sks1 = sks + i ' ' + sks2 ∧ st[r2 -- sks] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks → st[r2 -- sks2] .refval ≠ st[r2 -- sks] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDFORWARD : int-abs, , forward-le-05, ⊦ i < j ∧ 0 ≤ i → 0 < j])]]