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Proof step 22 from proof addclass-okarray (previous step)

¬ (¬ _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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
r ≠ jvmref ⊦ (addclass(class1, fis, st)[r -- sk]) = st[r -- sk]
Proof step 5:
⊦ is_arrayref(r, i, addclass(class1, fis, st)) ↔ is_arrayref(r, i, st)
Proof step 6:
⊦ oktype(val, ty, addclass(class1, fis, st)) ↔ oktype(val, ty, st)
Proof step 21:
is_integervalue(st[r -- _length]), is_arrayref(r, st[r -- _length] .intval, st), _length ∈ fis ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), addclass(class, fis, st)) ∧ r -- _length ∈ addclass(class, fis, st) ∧ 0 ≤ st[r -- _length] .intval ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → okval(st[r -- j '], ty)) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r -- _length ∈ st ∧ ¬ st[r -- _length] .intval < 0 ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → okval(st[r -- j '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkfs (class1, ty, `initstate' .field) ' ≠ _length], [CSIMPSEQ : ⊦ oktype(val, ty, st) ↔ okval(val, ty)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]