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Proof step 317 from proof hasSharing-put-index-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 316:
st[r -- sks1] = refval(r0) ∧ is_referencevalue(st[r -- sks1]), st[r -- (sks2 + i ' ' + sks)] = refval(r0), (st[r0 -- i ', refval(r2)][r -- (sks2 + i ' ' + sks)]) = refval(r3), (st[r0 -- i ', refval(r2)][r3 -- i ']) = refval(r4), (st[r0 -- i ', refval(r2)][r -- sks0]) = refval(r1), st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r2)][r4 -- sks3]) = refval(r1), st[r -- sks2] = refval(r0), sks1 + i ' ' ⊑ sks2, fits(r, sks2 + i ' ' + sks, st), fits(r4, sks3, st[r0 -- i ', refval(r2)]), is_referencevalue(st[r0 -- i ', refval(r2)][r3 -- (i ' ' + sks3)]), fits(r, sks0, st[r0 -- i ', refval(r2)]), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), ∀ sks. sks + i ' ' ⊑ sks2 → st[r -- sks] .refval ≠ r0, r2 = jvmref → is_reftype(ty), is_arraytype(st[r3 -- _type] .type) → 0 ≤ i ∧ i < st[r3 -- _length] .intval ⊦ sks0 = sks2 + (i ' ' + sks) + i ' ' + sks3, sks0 = [], r1 = jvmref, r = r2, r0 = jvmref, r3 = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), is_classtype(st[r3 -- _type] .type), ∃ sks0. ¬ (sks0 + i ' ' ⊑ sks2 + i ' ' + sks → st[r -- 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[r -- sks1], 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], [CSIMPNAMEDSEQ : javastore, , look-ins, ⊦ r ≠ r0 → (st[r0 -- sk0, val] [r -- sk ] ) = st[r -- sk]], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r -- sks1], r0)]]