Mathlib gotchas: Finsupp.degree is an AddMonoidHom; no MvPolynomial.coeff_mul_C

Finsupp.degree : (σ →₀ R) →+ R is a bundled AddMonoidHom, so there is no Finsupp.degree_add. Use map_add (for example rw [← hβs, map_add] after HasAntidiagonal.mem_antidiagonal). Finsupp.degree_apply unfolds it to ∑ i ∈ d.support, d i, and Finsupp.degree_eq_sum gives ∑ i, d i for a Fintype. For (p * C c).coeff β, MvPolynomial.coeff_mul_C is not available, so rewrite with mul_comm, coeff_C_mul, mul_comm. Inside rw, mem_antidiagonal is ambiguous between HasAntidiagonal.mem_antidiagonal and Finset.mem_antidiagonal; qualify it.