(def-theorem 1stnsquares "forall(n:zz, 0<=n implies sum(0,n,lambda(j:zz,j^2))=n*(n+1)*((2*n+1)/6))" (theory h-o-real-arithmetic) (proof ( (cut-with-single-formula "lambda(j:zz,j^2)==delta(lambda(n:zz,(n-1)*n*((2*n-1)/6)))") (backchain "with(a,b:[zz,rr], a==b)") (apply-macete-with-minor-premises tr%telescoping-prod-formula) simplify (unfold-single-defined-constant (0) rr%delta) simplify )))