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E_inv_RV -> E_opp_RV
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t6s committed Oct 21, 2021
1 parent d42966a commit c2ece80
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions probability/proba.v
Original file line number Diff line number Diff line change
Expand Up @@ -799,13 +799,13 @@ erewrite eq_bigr. (* to replace later with under *)
by rewrite exchange_big /=; apply: eq_bigr => i Hi.
Qed.

Lemma E_inv_RV (X : {RV P -> R}) : Ex P (- X)%ring = - `E X.
Lemma E_opp_RV (X : {RV P -> R}) : Ex P (- X)%ring = - `E X.
Proof.
by rewrite /Ex big_morph_oppR; apply eq_bigr => u _; rewrite -mulNR; congr (_ * _).
Qed.

Lemma E_sub_RV (X Y : {RV P -> R}) : `E (X `- Y) = `E X - `E Y.
Proof. by rewrite E_add_RV E_inv_RV. Qed.
Proof. by rewrite E_add_RV E_opp_RV. Qed.

Lemma E_const_RV k : `E (const_RV P k) = k.
Proof. by rewrite /Ex /const_RV /= -big_distrr /= FDist.f1 mulR1. Qed.
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