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Proof step 49 from proof hasSharing-pathex (previous step)

refs1 + r0 ' = st[r -- i '] .refval ' + refs0, 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, refs1 + r0 ', st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, hasSharing(r0, st), is_array(str, r, st), ∀ st, r, str, refs. # refs < # (refs1 + r0 ') → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ r = jvmref, hasSharing(r, st), r0 ≠ st[r -- i '] .refval ∧ ¬ r0 ∈ refs0, ¬ st[r -- i '] .refval ∈ refs1 ∧ st[r -- i '] .refval ≠ r0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 48:
st[r -- i '] = refval(r1), refs1 + r0 ' = r1 ' + refs0, 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, refs1 + r0 ', st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, hasSharing(r0, st), is_array(str, r, st), ∀ st, r, str, refs. # refs < # (refs1 + r0 ') → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ r = jvmref, hasSharing(r, st), r0 ≠ r1 ∧ ¬ r0 ∈ refs0, ¬ r1 ∈ refs1 ∧ r1 ≠ r0

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)]]