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Proof step 12 from proof union-okarray (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
st[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = intval(i), 0 ≤ i, r -- _length ∈ st, r -- _type ∈ st, ty0 ≤ ty, r ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r -- j ' ∈ st ⊦ r = jvmref, is_arrayref(r, i, st0 ∪ st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]