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Proof step 57 from proof hassharing-validrefs-dups (previous step)

0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, st[r -- i '] .refval ' + refs1, st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), validrefs(str, st[r -- i '] .refval ' + refs1, st[st[r -- i '] .refval -- _type] .type, st), hasSharing(st[r -- i '] .refval, st), ∀ st0, str, refs, r0. # (r0 ' + refs) < # (r ' + (st[r -- i '] .refval + refs1)) → (validrefs(str, r0 ' + refs, st0[r0 -- _type] .type, st0) → hasSharing(r0, st0) ∨ ¬ r0 ∈ refs ∧ ¬ dups(refs)) ⊦ r = jvmref, r ∈ refs1, hasSharing(r, st), ¬ st[r -- i '] .refval ∈ refs1 ∧ ¬ dups(refs1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 56:
st[r -- i '] = refval(r1), 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), validrefs(str, r1 ' + refs1, st[r1 -- _type] .type, st), hasSharing(r1, st), ∀ st0, str, refs, r0. # (r0 ' + refs) < # (r ' + (r1 + refs1)) → (validrefs(str, r0 ' + refs, st0[r0 -- _type] .type, st0) → hasSharing(r0, st0) ∨ ¬ r0 ∈ refs ∧ ¬ dups(refs)) ⊦ r = jvmref, r ∈ refs1, hasSharing(r, st), ¬ r1 ∈ refs1 ∧ ¬ dups(refs1)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- i '], r1] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- i '], r1)]]