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Proof step 20 from proof okarray-union (previous step)

ty0 ≤ mkarraytype(ty) ∧ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st0) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st0[r -- j '], ty, st0)), 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. ¬ j < 0 ∧ ¬ i ≤ j → r -- j ' ∈ st0) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st ∪ st0)), r = jvmref, r ∈ st .refs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty])]]