Theorems · Theorem · functional analysis
Balanced.smul_congr
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{s : Set E} {a b : 𝕜}, Balanced 𝕜 s → ‖a‖ = ‖b‖ → a • s = b • s- Defined in
- Mathlib.Analysis.LocallyConvex.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normstatement and proof · cited by 5,413
- Set.smulSetstatement · cited by 608
- Eq.leproof · cited by 605
- LE.le.antisymmproof · cited by 507
- Eq.geproof · cited by 375
- NormedDivisionRingstatement and proof · cited by 360
- Balancedstatement and proof · cited by 77
- Balanced.smul_monoproof · cited by 6
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