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Proof step 19 from proof okarray-union (previous step)

st0[r -- _length] = intval(i), st0[r -- _type] = typeval(ty0), r -- _type ∈ st0, r ∈ st0, 0 ≤ i, r -- _length ∈ st0, is_arraytype(ty0), ty0 .type ≤ ty, j < i, 0 ≤ j, 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r -- j ' ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st0) ⊦ r = jvmref, r ∈ st .refs, oktype(st0[r -- j '], ty, st ∪ st0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
ty0 = mkarraytype(ty1), st0[r -- _length] = intval(i), st0[r -- _type] = typeval(ty0), r -- _type ∈ st0, r ∈ st0, 0 ≤ i, r -- _length ∈ st0, is_arraytype(ty0), ty1 ≤ ty, j < i, 0 ≤ j, 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r -- j ' ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st0) ⊦ r = jvmref, r ∈ st .refs, oktype(st0[r -- j '], ty, st ∪ st0)

Rule argument

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

Additional information

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