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Proof step 33 from proof subset-okarray (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty0)), r ∈ st, ty0 ≤ ty, r -- _type ∈ st, is_arrayref(r, i, st), r -- _length ∈ st, 0 ≤ i, ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → okval(st[r -- j0 '], ty), r -- _length ∈ st → r -- _length ∈ st0 ∧ st[r -- _length] = st0[r -- _length], ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty0)), st0[r -- _length] = intval(i), r ∈ st0, r -- _length ∈ st0, 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), r -- _type ∈ st, ty0 ≤ ty, r ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → okval(st[r -- j0 '], ty), ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st0) ∧ is_arrayref(r, i, st0) ∧ (0 ≤ j ∧ j < i → okval(st0[r -- j '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ is_integervalue(intval(i))], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st])]]