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Proof step 15 from proof okarray-put-08 (previous step)

st[val .refval -- _length] = intval(i), is_referencevalue(val), val .refval -- _type ∈ st[r -- fs ', val0], is_typevalue(st[val .refval -- _type]), is_arraytype(st[val .refval -- _type] .type), st[val .refval -- _type] .type .type ≤ ty, val .refval -- _length ∈ st[r -- fs ', val0], is_arrayref(val .refval, i, st), j < i, val .refval -- _length ∈ st, val .refval -- _type ∈ st, val .refval ∈ st[r -- fs ', val0], 0 ≤ i, 0 ≤ j, 0 < i, val .refval ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[val .refval -- j '], ty) ⊦ fs ' = _length, fs ' = _type, val .refval = jvmref, okval(st[val .refval -- j '], ty)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
val = refval(r0), st[r0 -- _length] = intval(i), is_referencevalue(val), r0 -- _type ∈ st[r -- fs ', val0], is_typevalue(st[r0 -- _type]), is_arraytype(st[r0 -- _type] .type), st[r0 -- _type] .type .type ≤ ty, r0 -- _length ∈ st[r -- fs ', val0], is_arrayref(r0, i, st), j < i, r0 -- _length ∈ st, r0 -- _type ∈ st, r0 ∈ st[r -- fs ', val0], 0 ≤ i, 0 ≤ j, 0 < i, r0 ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r0 -- j '], ty) ⊦ fs ' = _length, fs ' = _type, r0 = jvmref, okval(st[r0 -- j '], ty)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [val, r0] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (val, r0)]]