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Proof step 9 from proof isarray-isarrayref (previous step)

st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty)), j < i0, 0 < i, 0 ≤ j, r -- _type ∈ st, i ≤ i0, r ∈ st, ∀ j. 0 ≤ j ∧ j < i0 → r -- j ' ∈ st, r -- _length ∈ st, 0 ≤ i0, j < i, 0 < i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, r -- j ' ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty)), j < i0, 0 < i, 0 ≤ j, r -- _type ∈ st, i ≤ i0, r ∈ st, r -- _length ∈ st, 0 ≤ i0, j < i, 0 < i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- j '], ty), ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → r -- j0 ' ∈ st ⊦ r = jvmref, r -- j ' ∈ st

Rule argument

[emptyarg]

Additional information

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