Theorems · Inductive type · functional analysis
IsRCLikeNormedField
(𝕜 : Type u_3) → [hk : NormedField 𝕜] → Prop
A mixin over a normed field, saying that the norm field structure is the same as ℝ or ℂ.
To endow such a field with a compatible RCLike structure in a proof, use
letI := IsRCLikeNormedField.rclike 𝕜.
- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 104 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- NormedField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedFieldstatement · cited by 1,084
Cited by113
Results whose statement or proof uses this declaration.
- IsRCLikeNormedField.rclikestatement and proof · cited by 29
- le_minSmoothnessproof · cited by 23
- Convex.norm_image_sub_le_of_norm_hasFDerivWithin_lestatement and proof · cited by 9
- ModelWithCorners.uniqueDiffOnproof · cited by 7
- minSmoothness_defstatement and proof · cited by 7
- implicitFunctionOfBivariatestatement and proof · cited by 6
- ModelWithCorners.convex_rangeproof · cited by 5
- ModelWithCorners.range_eq_univ_of_not_isRCLikeNormedFieldstatement and proof · cited by 5
- Convex.lipschitzOnWith_of_nnnorm_hasFDerivWithin_lestatement and proof · cited by 5
- hasStrictFDerivAt_uncurry_coprodstatement and proof · cited by 5
- ContDiffAt.isSymmSndFDerivAtproof · cited by 4
- hasFDerivAt_tsum_of_isPreconnectedstatement and proof · cited by 3