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| author | Cyril Cohen | 2016-08-25 01:38:44 +0200 |
|---|---|---|
| committer | Cyril Cohen | 2016-08-25 01:39:43 +0200 |
| commit | 2d824f394e8c3148e95b3374fb9903f6032ba3e6 (patch) | |
| tree | 6640dead8c6ee6147eebdc0c9e12bfa621787ced /mathcomp/character/classfun.v | |
| parent | 933085b944ecef3d50de3c81444079c30c462ca9 (diff) | |
Enriched numClosedFieldType so that it factors a lot of theory from both complex and algC.
The definitions of 'i, conjC, Re, Im, n.-root, sqrtC and their theory
have been moved to the numClosedFieldType structure in ssrnum.
This covers boths the uses in algC and complex.v. To that end the
numClosedFieldType structure has been enriched with conjugation and 'i.
Note that 'i can be deduced from the property of algebraic closure and is
only here to let the user chose which definitional equality should hold
on 'i. Same thing for conjC that could be written `|x|^+2/x, the only
nontrivial (up to my knowledge) property is the fact that conjugation
is a ring morphism.
Diffstat (limited to 'mathcomp/character/classfun.v')
| -rw-r--r-- | mathcomp/character/classfun.v | 3 |
1 files changed, 2 insertions, 1 deletions
diff --git a/mathcomp/character/classfun.v b/mathcomp/character/classfun.v index 4c27bd7..7473338 100644 --- a/mathcomp/character/classfun.v +++ b/mathcomp/character/classfun.v @@ -969,7 +969,8 @@ Lemma cfCauchySchwarz_sqrt phi psi : `|'[phi, psi]| <= sqrtC '[phi] * sqrtC '[psi] ?= iff ~~ free (phi :: psi). Proof. rewrite -(sqrCK (normr_ge0 _)) -sqrtCM ?qualifE ?cfnorm_ge0 //. -rewrite (mono_in_lerif ler_sqrtC) 1?rpredM ?qualifE ?normr_ge0 ?cfnorm_ge0 //. +rewrite (mono_in_lerif (@ler_sqrtC _)) 1?rpredM ?qualifE; +rewrite ?normr_ge0 ?cfnorm_ge0 //. exact: cfCauchySchwarz. Qed. |