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Proof step 32 from proof unchNorec-isarray (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _type] = typeval(mkarraytype(ty)), st[r -- _length] = st0[r -- _length], r ∈ st, okarray(r, ty, st), r -- _type ∈ st, unchangedNorec(r, st, st0), r -- _type ∈ st0, r ∈ st0, ∀ i. ¬ i < 0 ∧ ¬ st0[r -- _length] .intval ≤ i → st[r -- i '] = st0[r -- i '] ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st0) ∧ r ≠ jvmref ∧ r -- _length ∈ st0 ∧ is_integervalue(st0[r -- _length]) ∧ 0 ≤ st0[r -- _length] .intval ∧ is_arrayref(r, st0[r -- _length] .intval, st0) ∧ (∀ j. 0 ≤ j ∧ j < st0[r -- _length] .intval → oktype(st0[r -- j '], ty, st0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
st[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _type] = typeval(mkarraytype(ty)), st[r -- _length] = st0[r -- _length], r ∈ st, okarray(r, ty, st), r -- _type ∈ st, unchangedNorec(r, st, st0), r -- _type ∈ st0, r ∈ st0, ∀ i. ¬ i < 0 ∧ ¬ st0[r -- _length] .intval ≤ i → st[r -- i '] = st0[r -- i '] ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st0) ∧ r -- _length ∈ st0 ∧ is_integervalue(st0[r -- _length]) ∧ ¬ st0[r -- _length] .intval < 0 ∧ is_arrayref(r, st0[r -- _length] .intval, st0) ∧ (0 ≤ j ∧ j < st0[r -- _length] .intval → okval(st0[r -- j '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ oktype(val, ty, st) ↔ okval(val, ty)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]