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Proof step 247 from proof hasSharing-put-index-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 246:
st[r0 -- sks1] = refval(r) ∧ is_referencevalue(st[r0 -- sks1]), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r4)][r4 -- sks3]) = refval(r1), r = r0, (st[r0 -- i ', refval(r4)][r0 -- (sks1 + i ' ' + sks)]) = refval(r1), validref(str, r4, ty, st), disjoint(str, r0 ' + r4 ', st), fits(r4, sks3, st[r0 -- i ', refval(r4)]), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, fits(r0, sks1 + i ' ' + sks, st), ∀ sks0. sks0 + i ' ' ⊑ sks1 → st[r0 -- sks0] .refval ≠ r0 ⊦ sks3 = [], r4 = jvmref, r1 = jvmref, r0 = r4, r0 = jvmref, sks1 + i ' ' + sks = i ' ' + sks3, hasSharing(r0, st), hasSharing(r4, st), junkref(str, r0, st), ∃ sks0, sks2. sks1 + i ' ' + sks = sks0 + i ' ' + sks2 ∧ st[r0 -- sks0] .refval = r0 ∧ (∀ sks3. sks3 + i ' ' ⊑ sks0 → st[r0 -- sks3] .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[r0 -- sks1], r] 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[r0 -- sks1], r)]]