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Proof step 12 from proof add-okarray (previous step)

val = refval(r0) ∧ is_referencevalue(val), st[r0 -- _length] = intval(i), is_arrayref(r0, i, st), r0 -- _length ∈ st, 0 ≤ i, r0 ∈ st ⊦ r0 = jvmref, r = r0, okreftype(val, mkarraytype(ty0), addarray(r, ty, vals, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r0 -- j '], ty0, addarray(r, ty, vals, st))) ↔ okreftype(val, mkarraytype(ty0), st) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st[r0 -- j '], ty0, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ r ≠ r0 → (okreftype(refval(r), ty, addarray(r0, ty0, vals, st)) ↔ okreftype(refval(r), ty, st))
Proof step 11:
st[r0 -- _length] = intval(i), is_arrayref(r0, i, st), r0 -- _length ∈ st, 0 ≤ i, okreftype(refval(r0), mkarraytype(ty0), st), r0 ∈ st ⊦ r0 = jvmref, r = r0, (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r0 -- j '], ty0, addarray(r, ty, vals, st))) ↔ (∀ j. 0 ≤ j ∧ j < i → oktype(st[r0 -- j '], ty0, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]