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Proof step 37 from proof isarray-update (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), r -- _type ∈ st, r ∈ st, r -- _length ∈ st, is_integervalue(st[r -- _length]), 0 ≤ i ⊦ r = jvmref, r = r0, is_arrayref(r, i, update(r0, fis, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty)) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ is_arrayref(r, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → okval(st[r -- j '], ty))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
st[r -- _type] = typeval(mkarraytype(ty)), st[r -- _length] = intval(i), 0 ≤ i, r -- _length ∈ st, r ∈ st, r -- _type ∈ st ⊦ is_arrayref(r, i, update(r0, fis, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty)) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ is_arrayref(r, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → okval(st[r -- j '], ty)), r = r0, r = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_integervalue(intval(i))], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j])]]