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Proof step 13 from proof addobj-okarray (previous step)

⊦ r = r0, okreftype(refval(r), mkarraytype(ty), addobj(r0, class, fis, st)) ∧ r ≠ jvmref ∧ r -- _length ∈ addobj(r0, class, fis, st) ∧ is_integervalue(addobj(r0, class, fis, st)[r -- _length]) ∧ 0 ≤ (addobj(r0, class, fis, st)[r -- _length]) .intval ∧ is_arrayref(r, (addobj(r0, class, fis, st)[r -- _length]) .intval, addobj(r0, class, fis, st)) ∧ (∀ j. 0 ≤ j ∧ j < (addobj(r0, class, fis, st)[r -- _length]) .intval → oktype(addobj(r0, class, fis, st)[r -- j '], ty, addobj(r0, class, fis, st))) ↔ okarray(r, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ r ≠ r0 → (okreftype(refval(r), ty, addobj(r0, class1, fis, st)) ↔ okreftype(refval(r), ty, st))
Proof step 3:
⊦ r ≠ r0 → (r -- sk ∈ addobj(r0, class1, fis, st) ↔ r -- sk ∈ st)
Proof step 4:
⊦ r ≠ r0 → (addobj(r, class1, fis, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 5:
⊦ r ≠ r0 → (is_arrayref(r, i, addobj(r0, class1, fis, st)) ↔ is_arrayref(r, i, st))
Proof step 6:
⊦ oktype(val, ty, addobj(r, class, fis, st)) ↔ oktype(val, ty, st)
Proof step 12:
⊦ r = r0, 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. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → oktype(st[r -- j '], ty, st)) ↔ okarray(r, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]