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Proof step 70 from proof okarray-union-03 (previous step)

okarray(val, ty, i, st) ⊦ val .refval = jvmref, (0 ≤ j ∧ j < i → oktype((st0 ∪ st)[val .refval -- j '], ty, st0 ∪ st)) ∧ is_arrayref(val .refval, i, st0 ∪ st) ∧ ¬ i < 0 ∧ (st0 ∪ st)[val .refval -- _length] = intval(i) ∧ (val .refval -- _length ∈ st0 ∨ val .refval -- _length ∈ st) ∧ okreftype(val, mkarraytype(ty), st0 ∪ st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 69:
val = refval(r) ∧ is_referencevalue(val), okarray(val, ty, i, st) ⊦ r = jvmref, (0 ≤ j ∧ j < i → oktype((st0 ∪ st)[r -- j '], ty, st0 ∪ st)) ∧ is_arrayref(r, i, st0 ∪ st) ∧ ¬ i < 0 ∧ (st0 ∪ st)[r -- _length] = intval(i) ∧ (r -- _length ∈ st0 ∨ r -- _length ∈ st) ∧ okreftype(val, mkarraytype(ty), st0 ∪ st)

Rule argument

[speclemmaarg: is_referencevalue(val) ,r = val .refval ↔ val = refval(r) ,[val, r] → [val, r] ,T ,javavalue , ,elim-refval ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_referencevalue(val) → val .refval = jvmref], [CSIMPELIM : is_referencevalue(val) ⊦ r = val .refval ↔ val = refval(r)])], [EXTRATERMS : (val, r)]]