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# THe operation proof part of paper "Why and How zhSNARK works"

I'm reading the paper "Why and How zk-SNARK works" to learn zkSNARK, and I suffered some problem in section 4.4, when prove the ability of single operation.

In this section, it tries to come up with a protocol to verify that the prover have the ability of doing multiplication. It gives two number $$b$$ and $$c$$ and tries to verify the result of multiplication. The prover construct to polynomials $$l(x)$$ and $$r(x)$$ which satisfies: $$l(a)=b,\ r(a)=c$$ for some $$a$$ given by verifier, and get $$o(x)$$ that $$o(a)=b*c$$, the verifier needs to verify that $$p(x) = l(x)*r(x)-o(x)$$ has the zero point of $$a$$, which means the prover has the ability of multiplication.

While in the protocol mentioned at the end of section 4.4, there is nothing about the number $$b$$ and $$c$$, and the verifier doesn't verify the polynomial satisfies the properties like $$l(a)=b$$...So if I'm the prover, I can construct any polynomials if they satisfies $$l(x)*r(x)-o(x) = (x-a)h(x)$$, there is nothing about multiplication? I think I got something wrong but I really don't know what's it...