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fix and strengthen eq_bigmax and eq_bigmin #863

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Merged
affeldt-aist merged 1 commit into from
Mar 15, 2023
Merged

fix and strengthen eq_bigmax and eq_bigmin #863

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3 changes: 3 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -12,6 +12,9 @@

### Changed

- in `mathcomp_extra.v`
+ lemmas `eq_bigmax`, `eq_bigmin` changed to respect `P` in the returned type.

### Renamed

- in `lebesgue_measure.v`:
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12 changes: 8 additions & 4 deletions classical/mathcomp_extra.v
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Expand Up @@ -830,8 +830,10 @@ by apply/bigmax_leP; split => //; exact: PxF.
Qed.

Lemma eq_bigmax j P F : P j -> (forall i, P i -> x <= F i) ->
{i0 | i0 \in I & \big[max/x]_(i | P i) F i = F i0}.
Proof. by move=> Pi0 Hx; rewrite (bigmax_eq_arg Pi0) //; eexists. Qed.
{i0 | i0 \in P & \big[max/x]_(i | P i) F i = F i0}.
Proof.
by move=> Pi0 Hx; rewrite (bigmax_eq_arg Pi0) //; eexists => //; case:arg_maxP.
Qed.

Lemma le_bigmax2 P F1 F2 : (forall i, P i -> F1 i <= F2 i) ->
\big[max/x]_(i | P i) F1 i <= \big[max/x]_(i | P i) F2 i.
Expand Down Expand Up @@ -980,8 +982,10 @@ by apply/bigmin_geP; split => //; exact: PFx.
Qed.

Lemma eq_bigmin j P F : P j -> (forall i, P i -> F i <= x) ->
{i0 | i0 \in I & \big[min/x]_(i | P i) F i = F i0}.
Proof. by move=> Pi0 Hx; rewrite (bigmin_eq_arg Pi0) //; eexists. Qed.
{i0 | i0 \in P & \big[min/x]_(i | P i) F i = F i0}.
Proof.
by move=> Pi0 Hx; rewrite (bigmin_eq_arg Pi0) //; eexists => //; case:arg_minP.
Qed.

End bigmin_finType.

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