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Proof step 430 from proof hasSharing-put-index-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 429:
st[r3 -- sks3] = refval(r0) ∧ is_referencevalue(st[r3 -- sks3]), (st[r0 -- i ', refval(r3)][r3 -- (sks0 + i ' ' + sks)]) = refval(r1), st[r -- sks1] = refval(r0), st[r3 -- sks2] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), st[r3 -- sks0] = refval(r0), sks3 + i ' ' ⊑ sks0, fits(r3, sks0 + i ' ' + sks, st), i < st[r0 -- _length] .intval, 0 ≤ i, is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks0 + i ' ' + sks)]), fits(r3, sks2, st), is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks2)]), validref(str, r3, ty, st), disjoint(str, r ' + r3 ', st), fits(r, sks1, st), 0 < st[r0 -- _length] .intval, ∀ sks. sks + i ' ' ⊑ sks0 → st[r3 -- sks] .refval ≠ r0 ⊦ r3 = jvmref, sks2 = sks0 + i ' ' + sks, r1 = jvmref, r = r3, r0 = jvmref, sks1 = [], hasSharing(r, st), hasSharing(r3, st), junkref(str, r, st), ∃ sks, sks1. sks2 = sks + i ' ' + sks1 ∧ st[r3 -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r3 -- sks4] .refval ≠ st[r3 -- sks] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r0), ∃ sks, sks2. sks1 = sks + i ' ' + sks2 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks1 → st[r -- sks4] .refval ≠ r0), ∃ sks, sks4. sks1 = sks + i ' ' + sks4 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks → st[r -- sks5] .refval ≠ st[r -- 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[r3 -- 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[r3 -- sks3], r0)]]