Theorems · Theorem · functional analysis
Balanced.neg
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] {s : Set E},
Balanced 𝕜 s → Balanced 𝕜 (-s)- Defined in
- Mathlib.Analysis.LocallyConvex.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normproof · cited by 5,413
- LE.le.transproof · cited by 3,151
- SeminormedRingstatement and proof · cited by 446
- Set.negstatement · cited by 168
- Eq.subsetproof · cited by 124
- Balancedstatement · cited by 77
- forall₂_impproof · cited by 12
- Set.neg_subset_negproof · cited by 5
- Set.smul_set_negproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- balanced_negproof · cited by 0
- Balanced.subproof · cited by 0