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Proof step 13 from proof okarray-init-basic-01 (previous step)

⊦ r = r0, okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ st[r -- _length] = intval(i) ∧ 0 ≤ i ∧ is_arrayref(r, i, st) ∧ (∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → oktype(st[r -- j0 '], ty, st)) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(i) ∈ st ∧ 0 ≤ i ∧ is_arrayref(refval(r) .refval, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st[refval(r) .refval -- j '], ty, st)), is_classtype(ty), is_arraytype(ty)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
st[r -- _length] = intval(i), okreftype(refval(r), mkarraytype(ty), st), is_arrayref(r, i, st), r -- _length ∈ st, 0 ≤ i, r ∈ st ⊦ r = jvmref, r = r0, (∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → oktype(st[r -- j0 '], ty, st)) ↔ (∀ j. 0 ≤ j ∧ j < i → oktype(st[r -- j '], ty, st)), is_classtype(ty), is_arraytype(ty)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ ¬ ¬ (rk ∈ st ∧ st[rk] = val)], [CSIMPSEQ : ⊦ refval(r) .refval = r])]]