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Proof step 23 from proof union-okarray (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
st[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = intval(i), j < i, 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), r -- _type ∈ st, ty0 ≤ ty, r ∈ st, 0 ≤ j, 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, okval((st0 ∪ st)[r -- j '], ty)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j])]]