Theorems · Theorem · functional analysis
Module.Dual.im_extendRCLike_apply
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {F : Type u_2} [inst_1 : AddCommGroup F] [inst_2 : Module ℝ F] [inst_3 : Module 𝕜 F]
[inst_4 : IsScalarTower ℝ 𝕜 F] (g : Module.Dual ℝ F) (x : F), RCLike.im (g.extendRCLike x) = -g (RCLike.I • x)- Defined in
- Mathlib.Analysis.RCLike.Extend
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- AddMonoidHomstatement · cited by 3,230
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
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