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Proof step 11 from proof add-okarray (previous step)

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))

User applied rule case distinction

And obtained the following new goals

Proof step 8:
∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r0 -- j '], ty0, addarray(r, ty, vals, st)), st[r0 -- _length] = intval(i), is_arrayref(r0, i, st), r0 -- _length ∈ st, 0 ≤ i, okreftype(refval(r0), mkarraytype(ty0), st), r0 ∈ st ⊦ ∀ j. 0 ≤ j ∧ j < i → oktype(st[r0 -- j '], ty0, st), r0 = jvmref, r = r0
Proof step 10:
∀ j. 0 ≤ j ∧ j < i → oktype(st[r0 -- j '], ty0, st), st[r0 -- _length] = intval(i), is_arrayref(r0, i, st), r0 -- _length ∈ st, 0 ≤ i, okreftype(refval(r0), mkarraytype(ty0), st), r0 ∈ st ⊦ ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r0 -- j '], ty0, addarray(r, ty, vals, st)), r0 = jvmref, r = r0

Rule argument

[CASEDARG : pos: right 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]