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Theorem eqobjid

⊦ eqobjid(r, st, st0) ↔ (∀ sk. r -- sk ∈ st ↔ r -- sk ∈ st0) ∧ (r -- _type ∈ st → st[r -- _type] = st0[r -- _type]) ∧ (r -- _length ∈ st → st[r -- _length] = st0[r -- _length])