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Proof step 633 from proof hasSharing-put-index-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 632:
st[r1 -- sks0] = refval(r), st[r -- sks] = refval(r1), st[r -- _type] .type = mkarraytype(ty), fits(r1, sks0 + i ' ', st[r -- i ', refval(r1)]), fits(r, sks, st), disjoint(str, r ' + r1 ', st), validref(str, r1, ty, st), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval ⊦ i ' ' + sks0 + i ' ' = sks, r = jvmref, r = r1, sks = [], r1 = jvmref, sks0 = [], junkref(str, r, st), hasSharing(r1, st), hasSharing(r, st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks0 → st[r1 -- sks3] .refval ≠ r), ∃ sks2, sks4. sks0 = sks2 + i ' ' + sks4 ∧ st[r1 -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r1 -- sks3] .refval ≠ st[r1 -- sks2] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPNAMEDSEQ : store, javastore, At-same, ⊦ (st[rk, val][rk]) = val], [CSIMPNAMEDSEQ : storefuns, , lookup-one, ⊦ st[r -- sk '] = st[r -- sk]], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : list, storekeys, app, ⊦ sks + [] = sks])]]