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Proof step 22 from proof isarray-put (previous step)

st[r1 -- _type] = typeval(mkarraytype(ty0)), okval(val, ty), okarray(r1, ty0, st), r1 -- _type ∈ st, r1 ∈ st ⊦ r1 = jvmref, ty = void_type, mkfs(class, ty, fieldvar) ' = _length, okreftype(refval(r1), mkarraytype(ty0), st[r1 -- mkfs(class, ty, fieldvar) ', val]) ∧ r1 ≠ jvmref ∧ r1 -- _length ∈ st[r1 -- mkfs(class, ty, fieldvar) ', val] ∧ is_integervalue(st[r1 -- mkfs(class, ty, fieldvar) ', val][r1 -- _length]) ∧ 0 ≤ (st[r1 -- mkfs(class, ty, fieldvar) ', val][r1 -- _length]) .intval ∧ is_arrayref(r1, (st[r1 -- mkfs(class, ty, fieldvar) ', val][r1 -- _length]) .intval, st[r1 -- mkfs(class, ty, fieldvar) ', val]) ∧ (∀ j. 0 ≤ j ∧ j < (st[r1 -- mkfs(class, ty, fieldvar) ', val][r1 -- _length]) .intval → oktype(st[r1 -- mkfs(class, ty, fieldvar) ', val][r1 -- j '], ty0, st[r1 -- mkfs(class, ty, fieldvar) ', val]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ okarray(r, ty, st) → ¬ st[r -- _length] .intval < 0
Proof step 9:
⊦ ty0 ≠ void_type → (oktype(val, ty, st[r -- mkfs(class1, ty0, fieldvar0) ', val0]) ↔ oktype(val, ty, st))
Proof step 10:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 21:
st[r1 -- _type] = typeval(mkarraytype(ty0)), okval(val, ty), okarray(r1, ty0, st), r1 -- _type ∈ st, r1 ∈ st ⊦ r1 = jvmref, ty = void_type, mkfs(class, ty, fieldvar) ' = _length, okreftype(refval(r1), mkarraytype(ty0), st[r1 -- mkfs(class, ty, fieldvar) ', val]) ∧ r1 -- _length ∈ st ∧ is_integervalue(st[r1 -- _length]) ∧ is_arrayref(r1, st[r1 -- _length] .intval, st) ∧ (0 ≤ j ∧ j < st[r1 -- _length] .intval → okval(st[r1 -- j '], ty0))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([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])]]