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Proof step 12 from proof okarray-init-basic-01 (previous step)

st[r -- _length] = intval(i), okreftype(refval(r), mkarraytype(ty), st), is_arrayref(r, i, st), r -- _length ∈ st, 0 ≤ i, r ∈ st ⊦ r = jvmref, r = r0, (∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → oktype(st[r -- j0 '], ty, st)) ↔ (∀ j. 0 ≤ j ∧ j < i → oktype(st[r -- j '], ty, st)), is_classtype(ty), is_arraytype(ty)

User applied rule case distinction

And obtained the following new goals

Proof step 9:
∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → oktype(st[r -- j0 '], ty, st), st[r -- _length] = intval(i), okreftype(refval(r), mkarraytype(ty), st), is_arrayref(r, i, st), r -- _length ∈ st, 0 ≤ i, r ∈ st ⊦ ∀ j. 0 ≤ j ∧ j < i → oktype(st[r -- j '], ty, st), r = jvmref, r = r0, is_classtype(ty), is_arraytype(ty)
Proof step 11:
∀ j. 0 ≤ j ∧ j < i → oktype(st[r -- j '], ty, st), st[r -- _length] = intval(i), okreftype(refval(r), mkarraytype(ty), st), is_arrayref(r, i, st), r -- _length ∈ st, 0 ≤ i, r ∈ st ⊦ ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → oktype(st[r -- j0 '], ty, st), r = jvmref, r = r0, is_classtype(ty), is_arraytype(ty)

Rule argument

[CASEDARG : pos: right 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]