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Proof step 498 from proof hasSharing-put-index-refval (previous step)

st[r -- sks0] = refval(r1), st[st[r4 -- sks3] .refval -- _type] .type = mkarraytype(ty), (st[st[r4 -- sks3] .refval -- i ', refval(r4)][r4 -- (sks3 + (i ' ' + sks2) + i ' ' + sks4)]) = refval(r1), st[r -- sks1] = refval(st[r4 -- sks3] .refval), st[r4 -- (sks3 + i ' ' + sks2)] = refval(st[r4 -- sks3] .refval), (st[st[r4 -- sks3] .refval -- i ', refval(r4)][r4 -- (sks3 + i ' ' + sks2)]) = refval(r2), fits(r2, i ' ' + sks4, st[st[r4 -- sks3] .refval -- i ', refval(r4)]), i < st[st[r4 -- sks3] .refval -- _length] .intval, 0 ≤ i, is_referencevalue(st[st[r4 -- sks3] .refval -- i ', refval(r4)][st[r4 -- sks3] .refval -- (i ' ' + sks3 + (i ' ' + sks2) + i ' ' + sks4)]), fits(r, sks0, st), validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks1, st), fits(r4, sks3 + i ' ' + sks2, st), 0 < st[st[r4 -- sks3] .refval -- _length] .intval, ∀ sks. sks + i ' ' ⊑ sks3 → st[r4 -- sks] .refval ≠ st[r4 -- sks3] .refval ⊦ sks0 = [], r1 = jvmref, r = r4, st[r4 -- sks3] .refval = jvmref, r4 = jvmref, sks1 = [], sks0 = sks1 + i ' ' + sks3 + (i ' ' + sks2) + i ' ' + sks4, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r4 -- sks3] .refval), ∃ sks0, sks2. sks1 = sks0 + i ' ' + sks2 ∧ st[r -- sks0] .refval = st[r4 -- sks3] .refval ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks1, sks2. sks0 = sks1 + i ' ' + sks2 ∧ st[r -- sks1] .refval = st[r4 -- sks3] .refval ∧ (∀ sks4. sks4 + i ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ st[r -- sks1] .refval), ∃ sks. ¬ (sks + i ' ' ⊑ sks3 + i ' ' + sks2 → st[r4 -- sks] .refval ≠ st[r4 -- sks3] .refval), ∃ sks, sks5. sks3 + i ' ' + sks2 = sks + i ' ' + sks5 ∧ st[r4 -- sks] .refval = st[r4 -- sks3] .refval ∧ (∀ sks2. sks2 + i ' ' ⊑ sks → st[r4 -- sks2] .refval ≠ st[r4 -- sks] .refval)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 497:
st[r4 -- sks3] = refval(r0) ∧ is_referencevalue(st[r4 -- sks3]), st[r -- sks0] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r4 -- (sks3 + (i ' ' + sks2) + i ' ' + sks4)]) = refval(r1), st[r -- sks1] = refval(r0), st[r4 -- (sks3 + i ' ' + sks2)] = refval(r0), (st[r0 -- i ', refval(r4)][r4 -- (sks3 + i ' ' + sks2)]) = refval(r2), fits(r2, i ' ' + sks4, st[r0 -- i ', refval(r4)]), i < st[r0 -- _length] .intval, 0 ≤ i, is_referencevalue(st[r0 -- i ', refval(r4)][r0 -- (i ' ' + sks3 + (i ' ' + sks2) + i ' ' + sks4)]), fits(r, sks0, st), validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r, sks1, st), fits(r4, sks3 + i ' ' + sks2, st), 0 < st[r0 -- _length] .intval, ∀ sks. sks + i ' ' ⊑ sks3 → st[r4 -- sks] .refval ≠ r0 ⊦ sks0 = [], r1 = jvmref, r = r4, r0 = jvmref, r4 = jvmref, sks1 = [], sks0 = sks1 + i ' ' + sks3 + (i ' ' + sks2) + i ' ' + sks4, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r0), ∃ sks0, sks2. sks1 = sks0 + i ' ' + sks2 ∧ st[r -- sks0] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks0 → st[r -- sks4] .refval ≠ st[r -- sks0] .refval), ∃ sks1, sks2. sks0 = sks1 + i ' ' + sks2 ∧ st[r -- sks1] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ st[r -- sks1] .refval), ∃ sks. ¬ (sks + i ' ' ⊑ sks3 + i ' ' + sks2 → st[r4 -- sks] .refval ≠ r0), ∃ sks, sks5. sks3 + i ' ' + sks2 = sks + i ' ' + sks5 ∧ st[r4 -- sks] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks → st[r4 -- sks2] .refval ≠ st[r4 -- sks] .refval)

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-refval antecedent: is_referencevalue(val) succedent: r = val .refval ↔ val = refval(r) substlist: [val, r] → [st[r4 -- sks3], r0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : valuefuns, , refval-xtra, ⊦ ¬ is_referencevalue(val) → val .refval = jvmref], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r4 -- sks3], r0)]]