Theorems · Theorem · functional analysis
exists_norm_eq
∀ (E : Type u_1) [inst : SeminormedAddCommGroup E] [NormedSpace ℝ E] [NontrivialTopology E] {c : ℝ},
0 ≤ c → ∃ x, ‖x‖ = c- Cited by
- 4 results in Mathlib
- Foundations
- Depth 157 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.
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- inv_mul_cancel₀proof · cited by 267
- norm_smulproof · cited by 242
- Real.norm_of_nonnegproof · cited by 135
- norm_invproof · cited by 126
- norm_normproof · cited by 113
- NontrivialTopologystatement and proof · cited by 46
- exists_norm_ne_zeroproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- NormedSpace.sphere_nonemptyproof · cited by 8
- nnnorm_surjectiveproof · cited by 1
- range_normproof · cited by 0
- EuclideanGeometry.Sphere.inter_orthRadius_eq_empty_iffproof · cited by 0