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Proof step 15 from proof okarray-addarray-other (previous step)

st[r -- _length] = intval(i), r -- _length ∈ st, is_arrayref(r, i, st), r ∈ st, 0 ≤ i, j < i, 0 ≤ j, 0 < i, r -- _type ∈ st, is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type), st[r -- _type] .type .type ≤ ty, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st) ⊦ r = r0, r = jvmref, oktype(st[r -- j '], ty, addarray(r0, ty0, vals, st))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
st[r -- _type] .type = mkarraytype(ty1), st[r -- _length] = intval(i), r -- _length ∈ st, is_arrayref(r, i, st), r ∈ st, 0 ≤ i, j < i, 0 ≤ j, 0 < i, r -- _type ∈ st, is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type), ty1 ≤ ty, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st) ⊦ r = r0, r = jvmref, oktype(st[r -- j '], ty, addarray(r0, ty0, vals, st))

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [st[r -- _type] .type, ty1] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st[r -- _type] .type, ty1)]]