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Proof step 11 from proof okarray-1dim-basic-01 (previous step)

⊦ r = r0, okreftype(refval(r), mkarraytype(ty), addarray(r0, val0, i0, st)) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(i) ∈ addarray(r0, val0, i0, st) ∧ 0 ≤ i ∧ is_arrayref(refval(r) .refval, i, addarray(r0, val0, i0, st)) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(addarray(r0, val0, i0, st)[refval(r) .refval -- j '], ty, addarray(r0, val0, i0, st))) ↔ okarray(refval(r), ty, i, st), is_classtype(ty), is_arraytype(ty)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ r ≠ r0 → (okreftype(refval(r), ty, addarray(r0, val, i, st)) ↔ okreftype(refval(r), ty, st))
Proof step 3:
⊦ r ≠ r0 → (r -- sk ∈ addarray(r0, val, i, st) ↔ r -- sk ∈ st)
Proof step 4:
⊦ r ≠ r0 → (addarray(r, val, i, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 5:
⊦ r ≠ r0 → (is_arrayref(r, i, addarray(r0, val0, i0, st)) ↔ is_arrayref(r, i, st))
Proof step 6:
⊦ ¬ is_classtype(ty) ∧ ¬ is_arraytype(ty) → (oktype(val, ty, addarray(r0, val0, i0, st)) ↔ oktype(val, ty, st))
Proof step 10:
⊦ 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) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st)) ↔ okarray(refval(r), ty, i, st), is_classtype(ty), is_arraytype(ty)

Rule argument

[emptyarg]

Additional information

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