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Proof step 18 from proof isarray-addarray-01 (previous step)

st[r1 -- _type] = typeval(mkarraytype(ty0)), r1 ∈ st, r1 -- _type ∈ st, okreftype(refval(r1), mkarraytype(ty0), addarray(r0, ty, vals, st)) ∧ r1 ≠ jvmref ∧ r1 -- _length ∈ addarray(r0, ty, vals, st) ∧ is_integervalue(addarray(r0, ty, vals, st)[r1 -- _length]) ∧ 0 ≤ (addarray(r0, ty, vals, st)[r1 -- _length]) .intval ∧ is_arrayref(r1, (addarray(r0, ty, vals, st)[r1 -- _length]) .intval, addarray(r0, ty, vals, st)) ∧ (∀ j. 0 ≤ j ∧ j < (addarray(r0, ty, vals, st)[r1 -- _length]) .intval → oktype(addarray(r0, ty, vals, st)[r1 -- j '], ty0, addarray(r0, ty, vals, st))) ⊦ r1 = r0, r1 = jvmref, okarray(r1, ty0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ r ≠ r0 → (okreftype(refval(r), ty, addarray(r0, ty0, vals, st)) ↔ okreftype(refval(r), ty, st))
Proof step 9:
⊦ r ≠ r0 → (r -- sk ∈ addarray(r0, ty, vals, st) ↔ r -- sk ∈ st)
Proof step 10:
⊦ r ≠ r0 → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 11:
⊦ r ≠ r0 → (is_arrayref(r, i, addarray(r0, ty0, vals, st)) ↔ is_arrayref(r, i, st))
Proof step 17:
st[r1 -- _type] = typeval(mkarraytype(ty0)), r1 ∈ st, r1 -- _type ∈ st, okreftype(refval(r1), mkarraytype(ty0), st), r1 -- _length ∈ st, is_integervalue(st[r1 -- _length]), is_arrayref(r1, st[r1 -- _length] .intval, st), 0 ≤ st[r1 -- _length] .intval, ∀ j. ¬ j < 0 ∧ ¬ st[r1 -- _length] .intval ≤ j → oktype(st[r1 -- j '], ty0, addarray(r0, ty, vals, st)) ⊦ r1 = r0, r1 = jvmref, okarray(r1, ty0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]