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fixes #1208
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affeldt-aist committed Apr 16, 2024
1 parent c82da0e commit 388724c
Showing 1 changed file with 3 additions and 1 deletion.
4 changes: 3 additions & 1 deletion theories/measure.v
Original file line number Diff line number Diff line change
Expand Up @@ -3741,7 +3741,8 @@ Let caratheodory_decomp X :
mu (X `&` ~` A `&` B) + mu (X `&` ~` A `&` ~` B).
Proof. by rewrite mA mB [X in _ + _ + X = _]mB addeA. Qed.

Let caratheorody_decompIU X : mu (X `&` (A `|` B)) =
(* TODO: not used? *)
Let caratheodory_decompIU X : mu (X `&` (A `|` B)) =
mu (X `&` A `&` B) + mu (X `&` ~` A `&` B) + mu (X `&` A `&` ~` B).
Proof.
rewrite caratheodory_decomp -!addeA; congr (mu _ + _).
Expand All @@ -3765,6 +3766,7 @@ rewrite (setIC A) setIA setIC; apply/setIidPl.
- rewrite setIA setIC; apply/setIidPl; rewrite setIUl setICr set0U.
by move: AB; rewrite setIC => /disjoints_subset => AB; rewrite subsetI; split.
Qed.

End additive_ext_lemmas.

Lemma caratheodory_additive (A : (set T) ^nat) : (forall n, M (A n)) ->
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