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Proof step 43 from proof addclass-okarray (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ sk ∈ fis ∧ sk ≠ mkfs(class, void_type, `initstate' .field) ' → (addclass(class, fis, st)[r -- sk]) = st[r -- sk]
Proof step 22:
¬ (¬ _length ∈ fis ∧ _length ≠ mkfs(class, void_type, `initstate' .field) ') ⊦ okreftype(refval(r), mkarraytype(ty), addclass(class, fis, st)) ∧ r ≠ jvmref ∧ r -- _length ∈ addclass(class, fis, st) ∧ is_integervalue(addclass(class, fis, st)[r -- _length]) ∧ 0 ≤ (addclass(class, fis, st)[r -- _length]) .intval ∧ is_arrayref(r, (addclass(class, fis, st)[r -- _length]) .intval, addclass(class, fis, st)) ∧ (∀ j. 0 ≤ j ∧ j < (addclass(class, fis, st)[r -- _length]) .intval → oktype(addclass(class, fis, st)[r -- j '], ty, addclass(class, fis, st))) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))
Proof step 42:
¬ _length ∈ fis ∧ _length ≠ mkfs(class, void_type, `initstate' .field) ' ⊦ okreftype(refval(r), mkarraytype(ty), addclass(class, fis, st)) ∧ r ≠ jvmref ∧ r -- _length ∈ addclass(class, fis, st) ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, addclass(class, fis, st)) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(addclass(class, fis, st)[r -- j '], ty, addclass(class, fis, st))) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))

Rule argument

[crewrite-arg: ac-lookup-06 , F , [sk, r, st, fis, class] → [_length, r, st, fis, class] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (_length, r, st, fis, class)]]