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Lemma invf_ltp #1267

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Jul 30, 2024
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Lemma invf_ltp #1267

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Lemma invf_ltp
hoheinzollern Jul 24, 2024
cebf3b8
changelog
affeldt-aist Jul 29, 2024
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3 changes: 3 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -43,6 +43,9 @@
+ lemmas `lteD2rE`, `leeD2rE`
+ lemmas `lte_dD2rE`, `lee_dD2rE`

- in `mathcomp_extra.v`:
+ lemma `invf_ltp`

### Changed

- in `topology.v`:
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6 changes: 6 additions & 0 deletions classical/mathcomp_extra.v
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Expand Up @@ -63,6 +63,12 @@ Proof.
by move=> x y ? ?; rewrite -[in LHS](@invrK _ y) ltf_pV2// posrE invr_gt0.
Qed.

Lemma invf_ltp (F : numFieldType) :
{in Num.pos &, forall x y : F, (x < y^-1)%R = (y < x^-1)%R}.
Proof.
by move=> x y ? ?; rewrite -[in RHS](@invrK _ y) ltf_pV2// posrE invr_gt0.
Qed.

Definition proj {I} {T : I -> Type} i (f : forall i, T i) := f i.

Section DFunWith.
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