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Proof step 727 from proof hasSharing-put-index-refval (previous step)

st[r3 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r3), (st[r3 -- i ', refval(r4)][r4 -- (sks0 + i ' ' + sks3)]) = refval(r1), st[r4 -- sks0] = refval(r3), 0 < st[r3 -- _length] .intval, 0 ≤ i, i < st[r3 -- _length] .intval, validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks, st), fits(r, sks1, st), fits(r4, sks0, st), fits(r4, sks3, st[r3 -- i ', refval(r4)]) ⊦ sks1 = [], sks1 + i ' ' + sks0 + i ' ' + sks3 = sks, sks = [], r1 = jvmref, r = r4, r3 = jvmref, r4 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), is_referencevalue(refval(r)) ∧ validref(str, refval(r) .refval, mkclasstype(`java.lang.Object' .class), st) ∧ validreflist(str, refval(r4) ', mkclasstype(`java.lang.Object' .class), st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r3 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r3), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = r3 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks0 → st[r4 -- sks4] .refval ≠ r3), ∃ sks2, sks4. sks0 = sks2 + i ' ' + sks4 ∧ st[r4 -- sks2] .refval = r3 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks2 → st[r4 -- sks5] .refval ≠ st[r4 -- sks2] .refval)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 726:
st[r3 -- _type] .type = mkarraytype(ty), st[r -- sks] = refval(r1), st[r -- sks1] = refval(r3), (st[r3 -- i ', refval(r4)][r4 -- (sks0 + i ' ' + sks3)]) = refval(r1), st[r4 -- sks0] = refval(r3), 0 < st[r3 -- _length] .intval, 0 ≤ i, i < st[r3 -- _length] .intval, validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks, st), fits(r, sks1, st), fits(r4, sks0, st), fits(r4, sks3, st[r3 -- i ', refval(r4)]), validref(str, r4, mkclasstype(`java.lang.Object' .class), st) ⊦ sks1 = [], sks1 + i ' ' + sks0 + i ' ' + sks3 = sks, sks = [], r1 = jvmref, r = r4, r3 = jvmref, r4 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), validref(str, r, mkclasstype(`java.lang.Object' .class), st), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r3 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r3), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = r3 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks0 → st[r4 -- sks4] .refval ≠ r3), ∃ sks2, sks4. sks0 = sks2 + i ' ' + sks4 ∧ st[r4 -- sks2] .refval = r3 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks2 → st[r4 -- sks5] .refval ≠ st[r4 -- sks2] .refval)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : junkrefs, , validref-object-01, ⊦ ¬ validref (str, r, mkclasstype (`java.lang.Object' .class), st) ∧ r ≠ jvmref → ¬ validref(str, r, ty, st)], [CSIMPNAMEDSEQ : junkrefs, , validreflist-one-01, ⊦ validreflist (str, refval(r) ', ty, st) ↔ validref(str, r, ty, st)], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))])]]