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Proof step 33 from proof hasSharing-put-index-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
st[r2 -- sks1] = refval(r) ∧ is_referencevalue(st[r2 -- sks1]), (st[r -- i ', refval(r2)][r2 -- (sks1 + i ' ' + sks3)]) = refval(r0), st[r2 -- (sks1 + i ' ' + sks3)] = refval(r), (st[r -- i ', refval(r2)][r2 -- ((sks1 + i ' ' + sks3) + i ' ' + sks0)]) = refval(r2), st[r -- _type] .type = mkarraytype(ty), fits(r0, i ' ' + sks0, st[r -- i ', refval(r2)]), fits(r2, sks1 + i ' ' + sks3, st[r -- i ', refval(r2)]), validref(str, r2, ty, st), disjoint(str, r ' + r2 ', st), 0 ≤ i, i < st[r -- _length] .intval, 0 < st[r -- _length] .intval ⊦ r2 = jvmref, r = r2, r = jvmref, hasSharing(r, st), hasSharing(r2, st), junkref(str, r, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 → st[r2 -- sks2] .refval ≠ r), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks1 + i ' ' + sks3 → st[r2 -- sks2] .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[r2 -- 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], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (st[r2 -- sks1], r)]]