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Proof step 22 from proof hasSharing-put-index-refval (previous step)

st[r0 -- sks0] .refval = r0, (st[r0 -- i ', refval(r1)][r -- i ']) = refval(r2), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r1)][r0 -- ((sks0 + i ' ' + sks3) + i ' ' + sks1)]) = refval(r1), st[r0 -- (sks0 + i ' ' + sks3)] = refval(r0), (st[r0 -- i ', refval(r1)][r0 -- (sks0 + i ' ' + sks3)]) = refval(r), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, disjoint(str, r0 ' + r1 ', st), validref(str, r1, ty, st), fits(r0, sks0 + i ' ' + sks3, st[r0 -- i ', refval(r1)]), fits(r2, sks1, st[r0 -- i ', refval(r1)]), is_arraytype(st[r -- _type] .type) → i < st[r -- _length] .intval ⊦ (sks0 + i ' ' + sks3) + i ' ' + sks1 = i ' ', r0 = jvmref, r0 = r1, r1 = jvmref, r = jvmref, junkref(str, r0, st), hasSharing(r1, st), hasSharing(r0, st), is_classtype(st[r -- _type] .type), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks0 → st[r0 -- sks2] .refval ≠ r0), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks0 + i ' ' + sks3 → st[r0 -- sks2] .refval ≠ r0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
st[r0 -- sks0] = refval(r3) ∧ is_referencevalue(st[r0 -- sks0]), r3 = r0, (st[r0 -- i ', refval(r1)][r -- i ']) = refval(r2), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r1)][r0 -- ((sks0 + i ' ' + sks3) + i ' ' + sks1)]) = refval(r1), st[r0 -- (sks0 + i ' ' + sks3)] = refval(r0), (st[r0 -- i ', refval(r1)][r0 -- (sks0 + i ' ' + sks3)]) = refval(r), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, disjoint(str, r0 ' + r1 ', st), validref(str, r1, ty, st), fits(r0, sks0 + i ' ' + sks3, st[r0 -- i ', refval(r1)]), fits(r2, sks1, st[r0 -- i ', refval(r1)]), is_arraytype(st[r -- _type] .type) → i < st[r -- _length] .intval ⊦ (sks0 + i ' ' + sks3) + i ' ' + sks1 = i ' ', r0 = jvmref, r0 = r1, r1 = jvmref, r = jvmref, junkref(str, r0, st), hasSharing(r1, st), hasSharing(r0, st), is_classtype(st[r -- _type] .type), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks0 → st[r0 -- sks2] .refval ≠ r0), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks0 + i ' ' + sks3 → st[r0 -- sks2] .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 -- sks0], r3] 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 -- sks0], r3)]]