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Proof step 26 from proof okarray-union (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 25:
st0[r -- _type] = typeval(ty0), st0[r -- _length] = intval(i), r -- _length ∈ st0, 0 ≤ i, r ∈ st0, r -- _type ∈ st0, is_typevalue(st0[r -- _type]) ⊦ r = jvmref, is_arraytype(ty0) ∧ ty0 .type ≤ ty ∧ is_arrayref(r, i, st ∪ st0) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st ∪ st0)) ↔ ty0 ≤ mkarraytype(ty) ∧ is_arrayref(r, i, st0) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st0[r -- j '], ty, st0)), r ∈ st .refs

Rule argument

[speclemmaarg: ,is_typevalue(val) → (ty = val .type ↔ val = typeval(ty)) ,[val, ty] → [st0[r -- _type], ty0] ,T ,javavalue , ,elim-10 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_typevalue(val) → ( ty = val .type ↔ val = typeval(ty))])], [EXTRATERMS : (st0[r -- _type], ty0)]]