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Proof step 13 from proof okarray-put-samefield-01 (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty1)), is_arrayref(r, i, st), r -- _length ∈ st, ty1 ≤ ty, r -- _type ∈ st, r ∈ st, okval(val, ty0), okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), r -- mkfs(class, ty0, fieldvar) ' ∈ st, 0 ≤ i, ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, okreftype(refval(r), mkarraytype(ty), st) ∧ (0 ≤ j ∧ j < i → okval(st[r -- j '], ty))

User applied rule case distinction

And obtained the following new goals

Proof step 12:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty1)), is_arrayref(r, i, st), r -- _length ∈ st, ty1 ≤ ty, r -- _type ∈ st, r ∈ st, okval(val, ty0), okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), r -- mkfs(class, ty0, fieldvar) ' ∈ st, 0 ≤ i, ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ okreftype(refval(r), mkarraytype(ty), st), r = jvmref, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length

Rule argument

[CASEDARG : pos: right 4, ()]

Additional information

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