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Proof step 13 from proof ac-okarray-01 (previous step)

⊦ val = refval(jvmref), okreftype(val, mkarraytype(ty), addclass(class, fis, st)) ∧ val .refval ≠ jvmref ∧ (val .refval -- _length) × intval(i) ∈ addclass(class, fis, st) ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, addclass(class, fis, st)) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(addclass(class, fis, st)[val .refval -- j '], ty, addclass(class, fis, st))) ↔ okarray(val, ty, i, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ val ≠ refval(jvmref) → (okreftype(val, ty, addclass(class1, fis, st)) ↔ okreftype(val, ty, st))
Proof step 3:
r ≠ jvmref ⊦ (addclass(class1, fis, st)[r -- sk]) = st[r -- sk]
Proof step 4:
⊦ is_arrayref(r, i, addclass(class1, fis, st)) ↔ is_arrayref(r, i, st)
Proof step 5:
⊦ oktype(val, ty, addclass(class1, fis, st)) ↔ oktype(val, ty, st)
Proof step 12:
⊦ val = refval(jvmref), okreftype(val, mkarraytype(ty), st) ∧ val .refval ≠ jvmref ∧ val .refval -- _length ∈ addclass(class, fis, st) ∧ st[val .refval -- _length] = intval(i) ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[val .refval -- j '], ty, st)) ↔ okarray(val, ty, i, st)

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])]]