My question is that, suppose there is a txn tx(k) paid from user u to v, that refers two txns tx(i) and tx(j) as it's inputs. Also, both these inputs are meant for different public keys of u, say, Pk1(u) and Pk2(u).
How does u sign tx(k) for v, i.e. how does she convince v that she owns both of those public keys? Does she sign tx(k) with both Sk1(u) and Sk2(u)?