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Proof step 395 from proof hasSharing-put-index-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 394:
st[r3 -- sks0] = refval(r0) ∧ is_referencevalue(st[r3 -- sks0]), st[r -- sks1] = refval(r0), (st[r0 -- i ', refval(r3)][r3 -- sks3]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r3)][r3 -- (sks0 + i ' ' + sks)]) = refval(r1), is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks3)]), 0 ≤ i, i < st[r0 -- _length] .intval, fits(r3, sks3, st[r0 -- i ', refval(r3)]), fits(r, sks1, st), disjoint(str, r ' + r3 ', st), validref(str, r3, ty, st), is_referencevalue(st[r0 -- i ', refval(r3)][r0 -- (i ' ' + sks0 + i ' ' + sks)]), fits(r3, sks0 + i ' ' + sks, st), 0 < st[r0 -- _length] .intval, ∀ sks2. sks2 + i ' ' ⊑ sks0 → st[r3 -- sks2] .refval ≠ r0 ⊦ sks1 = [], r0 = jvmref, r = r3, r1 = jvmref, sks0 + i ' ' + sks = sks3, r3 = jvmref, junkref(str, r, st), hasSharing(r3, st), hasSharing(r, st), ∃ sks, sks4. sks1 = sks + i ' ' + sks4 ∧ st[r -- sks] .refval = r0 ∧ (∀ sks5. sks5 + i ' ' ⊑ sks → st[r -- sks5] .refval ≠ st[r -- sks] .refval), ∃ sks4. ¬ (sks4 + i ' ' ⊑ sks1 → st[r -- sks4] .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), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r -- sks2] .refval ≠ r0), ∃ sks2, sks5. sks0 + i ' ' + sks = sks2 + i ' ' + sks5 ∧ st[r3 -- sks2] .refval = r0 ∧ (∀ sks4. sks4 + i ' ' ⊑ sks2 → st[r3 -- sks4] .refval ≠ st[r3 -- sks2] .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 -- sks0], 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 -- sks0], r0)]]