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Proof step 11 from proof okarray-put-07 (previous step)

st[r0 -- _length] = intval(i), st[r0 -- _type] = typeval(mkarraytype(ty0)), 0 ≤ i, r0 -- _type ∈ st, ty0 ≤ ty, r0 -- _length ∈ st, is_arrayref(r0, i, st), r0 ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r0 -- j '], ty) ⊦ r0 = jvmref, r = r0, okreftype(refval(r0), mkarraytype(ty), st) ∧ refval(r0) .refval ≠ jvmref ∧ (refval(r0) .refval -- _length) × intval(i) ∈ st ∧ 0 ≤ i ∧ is_arrayref(refval(r0) .refval, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st[refval(r0) .refval -- j '], ty, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 10:
st[r0 -- _length] = intval(i), st[r0 -- _type] = typeval(mkarraytype(ty0)), 0 ≤ i, r0 -- _type ∈ st, ty0 ≤ ty, r0 -- _length ∈ st, is_arrayref(r0, i, st), r0 ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r0 -- j '], ty) ⊦ r0 = jvmref, r = r0, okreftype(refval(r0), mkarraytype(ty), st) ∧ (0 ≤ j ∧ j < i → okval(st[r0 -- j '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ refval(r) .refval = r])]]