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Proof step 261 from proof hasSharing-put-index-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 260:
st[r4 -- sks3] = refval(r) ∧ is_referencevalue(st[r4 -- sks3]), st[r -- _type] .type = mkarraytype(ty), st[r -- sks0] = refval(r1), (st[r -- i ', refval(r4)][r0 -- i ']) = refval(r2), (st[r -- i ', refval(r4)][r4 -- (sks3 + i ' ' + sks2)]) = refval(r0), st[r4 -- (sks3 + i ' ' + sks2)] = refval(r), (st[r -- i ', refval(r4)][r4 -- (sks3 + (i ' ' + sks2) + i ' ' + sks1)]) = refval(r1), disjoint(str, r ' + r4 ', st), validref(str, r4, ty, st), fits(r, sks0, st), i < st[r -- _length] .intval, 0 ≤ i, fits(r2, sks1, st[r -- i ', refval(r4)]), fits(r4, sks3 + i ' ' + sks2, st), 0 < st[r -- _length] .intval, is_arraytype(st[r0 -- _type] .type) → i < st[r0 -- _length] .intval, ∀ sks. sks + i ' ' ⊑ sks3 → st[r4 -- sks] .refval ≠ r ⊦ r = jvmref, r = r4, r1 = jvmref, sks0 = [], r0 = jvmref, r4 = jvmref, sks0 = i ' ' + sks3 + (i ' ' + sks2) + i ' ' + sks1, is_classtype(st[r0 -- _type] .type), junkref(str, r, st), hasSharing(r4, st), hasSharing(r, st), ∃ sks2, sks1. sks0 = sks2 + i ' ' + sks1 ∧ st[r -- sks2] .refval = r ∧ (∀ sks. sks + i ' ' ⊑ sks2 → st[r -- sks] .refval ≠ r), ∃ sks, sks4. sks3 + i ' ' + sks2 = sks + i ' ' + sks4 ∧ st[r4 -- sks] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks → st[r4 -- sks2] .refval ≠ st[r4 -- sks] .refval), ∃ sks. ¬ (sks + i ' ' ⊑ sks3 + i ' ' + sks2 → st[r4 -- sks] .refval ≠ r)

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[r4 -- sks3], 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 : 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[r4 -- sks3], r)]]