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theories/esum.v

Lines changed: 3 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -493,7 +493,7 @@ Let ge0_esumZ c : 0 <= c -> (forall t, A t -> 0 <= f t) ->
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Proof.
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rewrite le_eqVlt => /predU1P[<- _|c0 f0].
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by rewrite mul0e esum1// => ? _; rewrite mul0e.
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rewrite ge0_esum; first by move=> x /f0 ax0; rewrite ?mule_ge0// ltW.
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rewrite [in LHS]ge0_esum; first by move=> x /f0 ax0; rewrite ?mule_ge0// ltW.
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by rewrite ge0_esum//; apply: PosEsum.pos_esumZ => //; exact: ltW.
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Qed.
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@@ -521,7 +521,8 @@ Lemma esumD {R : realType} {T : choiceType} (I : set T) (f g : T -> \bar R) :
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(forall i, I i -> 0 <= f i) -> (forall i, I i -> 0 <= g i) ->
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\esum_(i in I) (f i + g i) = \esum_(i in I) f i + \esum_(i in I) g i.
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Proof.
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move=> f0 g0; rewrite ge0_esum//; first by move=> *; rewrite adde_ge0 ?f0 ?g0.
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move=> f0 g0; rewrite [in LHS]ge0_esum//.
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by move=> *; rewrite adde_ge0 ?f0 ?g0.
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by do 2 rewrite ge0_esum//; exact: PosEsum.pos_esumD.
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Qed.
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