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Proof step 12 from proof okarray-put-badfield (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty0)), r ∈ st, ty0 ≤ ty, r -- _type ∈ st, is_arrayref(r, i, st), r -- _length ∈ st, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, fs ' = _type, fs ' = _length, okreftype(refval(r), mkarraytype(ty), st[r -- fs ', val]) ∧ r ≠ jvmref ∧ r -- _length ∈ st[r -- fs ', val] ∧ is_integervalue(st[r -- fs ', val][r -- _length]) ∧ 0 ≤ (st[r -- fs ', val][r -- _length]) .intval ∧ is_arrayref(r, (st[r -- fs ', val][r -- _length]) .intval, st[r -- fs ', val]) ∧ (∀ j. 0 ≤ j ∧ j < (st[r -- fs ', val][r -- _length]) .intval → oktype(st[r -- fs ', val][r -- j '], ty, st[r -- fs ', val]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ sk0 ≠ _type → (oktype(val, ty, st[r -- sk0, val0]) ↔ oktype(val, ty, st))
Proof step 7:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 11:
st[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = intval(i), 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), r -- _type ∈ st, ty0 ≤ ty, r ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ fs ' = _length, fs ' = _type, r = jvmref, okreftype(refval(r), mkarraytype(ty), st[r -- fs ', val]) ∧ (0 ≤ j ∧ j < i → okval(st[r -- j '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ is_integervalue(intval(i))], [CSIMPSEQ : ⊦ (st[r0 -- fs ', val][r -- i ']) = st[r -- i ']], [CSIMPSEQ : ⊦ is_arrayref (r, i, st[r0 -- fs ', val]) ↔ is_arrayref(r, i, st)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st])]]