Section IntegralOverComRing.
Variables (R K : comRingType) (RtoK : {rmorphism R -> K}).
Let integral0_RtoK := integral0 RtoK.
Let integral1_RtoK := integral1 RtoK.
Let monicXsubC_K := @monicXsubC K.
Hint Resolve integral0_RtoK integral1_RtoK monicXsubC_K : core.
Let XsubC0 (u : K) : root ('X - u%:P) u. Proof. by rewrite root_XsubC. Qed.
Let intR_XsubC u :
integralOver RtoK (- u) -> {in 'X - u%:P : seq K, integralRange RtoK}.

Lemma integral_add u v :
integralOver RtoK u -> integralOver RtoK v -> integralOver RtoK (u + v).