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

st0[r -- _length] = intval(i), st0[r -- _type] = typeval(mkarraytype(ty1)), ty1 ≤ ty, r -- _type ∈ st0, r ∈ st0, 0 ≤ i, r -- _length ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r -- j ' ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st ∪ st0) ⊦ r = jvmref, r ∈ st .refs, (0 ≤ j ∧ j < i → r -- j ' ∈ st0) ∧ (0 ≤ j0 ∧ j0 < i → oktype(st0[r -- j0 '], ty, st0))

User applied rule case distinction

And obtained the following new goals

Proof step 8:
st0[r -- _length] = intval(i), st0[r -- _type] = typeval(mkarraytype(ty1)), ty1 ≤ ty, r -- _type ∈ st0, r ∈ st0, 0 ≤ i, r -- _length ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r -- j ' ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st ∪ st0) ⊦ 0 ≤ j ∧ j < i → r -- j ' ∈ st0, r = jvmref, r ∈ st .refs
Proof step 11:
st0[r -- _length] = intval(i), st0[r -- _type] = typeval(mkarraytype(ty1)), ty1 ≤ ty, r -- _type ∈ st0, r ∈ st0, 0 ≤ i, r -- _length ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r -- j ' ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st ∪ st0) ⊦ 0 ≤ j0 ∧ j0 < i → oktype(st0[r -- j0 '], ty, st0), r = jvmref, r ∈ st .refs

Rule argument

[CASEDARG : pos: right 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]