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Proof step 720 from proof hasSharing-put-index-refval (previous step)

st[r -- sks1] = refval(st[r2 -- sks4] .refval), st[r -- sks] = refval(r1), st[st[r2 -- sks4] .refval -- _type] .type = mkarraytype(ty), (st[st[r2 -- sks4] .refval -- i ', refval(r2)][r3 -- i ']) = refval(r4), (st[st[r2 -- sks4] .refval -- i ', refval(r2)][r2 -- (sks4 + i ' ' + sks2)]) = refval(r3), st[r2 -- (sks4 + i ' ' + sks2)] = refval(st[r2 -- sks4] .refval), (st[st[r2 -- sks4] .refval -- i ', refval(r2)][r2 -- (sks4 + (i ' ' + sks2) + i ' ' + sks3)]) = refval(r1), fits(r, sks1, st), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[st[r2 -- sks4] .refval -- _length] .intval, 0 ≤ i, fits(r4, sks3, st[st[r2 -- sks4] .refval -- i ', refval(r2)]), fits(r2, sks4 + i ' ' + sks2, st), 0 < st[st[r2 -- sks4] .refval -- _length] .intval, is_arraytype(st[r3 -- _type] .type) → i < st[r3 -- _length] .intval, ∀ sks0. sks0 + i ' ' ⊑ sks4 → st[r2 -- sks0] .refval ≠ st[r2 -- sks4] .refval ⊦ sks1 = [], r3 = jvmref, r2 = jvmref, st[r2 -- sks4] .refval = jvmref, r = r2, r1 = jvmref, sks = [], sks1 + i ' ' + sks4 + (i ' ' + sks2) + i ' ' + sks3 = sks, is_classtype(st[r3 -- _type] .type), junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = st[r2 -- sks4] .refval ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ st[r2 -- sks4] .refval), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = st[r2 -- sks4] .refval ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks0, sks6. sks4 + i ' ' + sks2 = sks0 + i ' ' + sks6 ∧ st[r2 -- sks0] .refval = st[r2 -- sks4] .refval ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r2 -- sks5] .refval ≠ st[r2 -- sks0] .refval), ∃ sks0. ¬ (sks0 + i ' ' ⊑ sks4 + i ' ' + sks2 → st[r2 -- sks0] .refval ≠ st[r2 -- sks4] .refval)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 719:
st[r2 -- sks4] = refval(r0) ∧ is_referencevalue(st[r2 -- sks4]), st[r -- sks1] = refval(r0), st[r -- sks] = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r3 -- i ']) = refval(r4), (st[r0 -- i ', refval(r2)][r2 -- (sks4 + i ' ' + sks2)]) = refval(r3), st[r2 -- (sks4 + i ' ' + sks2)] = refval(r0), (st[r0 -- i ', refval(r2)][r2 -- (sks4 + (i ' ' + sks2) + i ' ' + sks3)]) = refval(r1), fits(r, sks1, st), fits(r, sks, st), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st), i < st[r0 -- _length] .intval, 0 ≤ i, fits(r4, sks3, st[r0 -- i ', refval(r2)]), fits(r2, sks4 + i ' ' + sks2, st), 0 < st[r0 -- _length] .intval, is_arraytype(st[r3 -- _type] .type) → i < st[r3 -- _length] .intval, ∀ sks0. sks0 + i ' ' ⊑ sks4 → st[r2 -- sks0] .refval ≠ r0 ⊦ sks1 = [], r3 = jvmref, r2 = jvmref, r0 = jvmref, r = r2, r1 = jvmref, sks = [], sks1 + i ' ' + sks4 + (i ' ' + sks2) + i ' ' + sks3 = sks, is_classtype(st[r3 -- _type] .type), junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks, sks3. sks1 = sks + i ' ' + sks3 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks → st[r -- sks4] .refval ≠ st[r -- sks] .refval), ∃ sks3. ¬ (sks3 + i ' ' ⊑ sks1 → st[r -- sks3] .refval ≠ r0), ∃ sks1, sks3. sks = sks1 + i ' ' + sks3 ∧ st[r -- sks1] .refval = r0 ∧ (∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ st[r -- sks1] .refval), ∃ sks0, sks6. sks4 + i ' ' + sks2 = sks0 + i ' ' + sks6 ∧ st[r2 -- sks0] .refval = r0 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks0 → st[r2 -- sks5] .refval ≠ st[r2 -- sks0] .refval), ∃ sks0. ¬ (sks0 + i ' ' ⊑ sks4 + i ' ' + sks2 → st[r2 -- sks0] .refval ≠ r0)

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[r2 -- sks4], 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 : javastore, , look-ins, ⊦ r ≠ r0 → (st[r0 -- sk0, val] [r -- sk ] ) = st[r -- sk]], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r2 -- sks4], r0)]]