Theorems · Theorem · functional analysis
exists_forall_closed_ball_dist_add_le_two_sub
∀ (E : Type u_1) [inst : SeminormedAddCommGroup E] [UniformConvexSpace E] {ε : ℝ} [NormedSpace ℝ E],
0 < ε → ∃ δ, 0 < δ ∧ ∀ ⦃x : E⦄, ‖x‖ ≤ 1 → ∀ ⦃y : E⦄, ‖y‖ ≤ 1 → ε ≤ ‖x - y‖ → ‖x + y‖ ≤ 2 - δ- Defined in
- Mathlib.Analysis.Convex.Uniform
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites48
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
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- LT.lt.ne'proof · cited by 1,417
- one_smulproof · cited by 1,374
- add_assocproof · cited by 746
Cited by1
Results whose statement or proof uses this declaration.
- exists_forall_closed_ball_dist_add_le_two_mul_subproof · cited by 0