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Proof step 540 from proof hasSharing-put-index-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 539:
st[r -- sks0] = refval(r1), st[r3 -- _type] .type = mkarraytype(ty), st[r4 -- sks3] = refval(r1), st[r -- sks1] = refval(r3), is_referencevalue(st[r3 -- i ', refval(r4)][r3 -- (i ' ' + sks3)]), fits(r, sks0, st), validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks1, st), fits(r4, sks3, st), i < st[r3 -- _length] .intval, 0 ≤ i, 0 < st[r3 -- _length] .intval, r4 = jvmref → is_reftype(ty) ⊦ sks1 = [], sks0 = sks1 + i ' ' + sks3, sks0 = [], r1 = jvmref, r = r4, r3 = jvmref, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r3), ∃ sks, sks2. sks1 = sks + i ' ' + sks2 ∧ st[r -- sks] .refval = r3 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks, sks2. sks0 = sks + i ' ' + sks2 ∧ st[r -- sks] .refval = r3 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks, sks4. sks3 = sks + i ' ' + sks4 ∧ st[r4 -- sks] .refval = r3 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks → st[r4 -- sks2] .refval ≠ st[r4 -- sks] .refval), validref(str, r, mkclasstype(`java.lang.Object' .class), st) ∧ validref(str, r4, mkclasstype(`java.lang.Object' .class), st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([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))])]]