proposition: Lemma sum_seq1 S x : (forall y, S y != 0 -> x == y) -> sum S = S x.
proof: Proof. move=> domS; rewrite (sum_finseq (r := [:: x])) //. by move=> y; rewrite !inE => /domS /eqP->. by rewrite big_seq1. Qed.
imports: mathcomp(all_ssreflect all_algebra) mathcomp.classical(boolp) xfinmap ereal reals discrete realseq mathcomp.classical(classical_sets functions mathcomp_extra) topology