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Proof step 293 from proof hasSharing-put-index-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 292:
st[r4 -- sks1] = refval(r) ∧ is_referencevalue(st[r4 -- sks1]), st[r -- sks0] = refval(r1), st[r -- _type] .type = mkarraytype(ty), (st[r -- i ', refval(r4)][r4 -- (sks1 + i ' ' + sks)]) = refval(r1), 0 ≤ i, i < st[r -- _length] .intval, fits(r, sks0, st), validref(str, r4, ty, st), disjoint(str, r ' + r4 ', st), fits(r4, sks1 + i ' ' + sks, st), 0 < st[r -- _length] .intval, ∀ sks2. sks2 + i ' ' ⊑ sks1 → st[r4 -- sks2] .refval ≠ r ⊦ r4 = jvmref, sks0 = [], r1 = jvmref, r = r4, r = jvmref, sks0 = i ' ' + sks1 + i ' ' + sks, hasSharing(r, st), hasSharing(r4, st), junkref(str, r, st), ∃ sks, sks2. sks0 = sks + i ' ' + sks2 ∧ st[r -- sks] .refval = r ∧ (∀ sks2. sks2 + i ' ' ⊑ sks → st[r -- sks2] .refval ≠ r), ∃ sks2, sks3. sks1 + i ' ' + sks = sks2 + i ' ' + sks3 ∧ st[r4 -- sks2] .refval = r ∧ (∀ sks. sks + i ' ' ⊑ sks2 → st[r4 -- sks] .refval ≠ st[r4 -- 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[r4 -- 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[r4 -- sks1], r)]]