Theorems · Theorem · functional analysis
exists_dist_lt_le
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [NormedSpace ℝ E] {x z : E} {δ ε : ℝ},
0 < δ → 0 ≤ ε → dist x z < ε + δ → ∃ y, dist x y < δ ∧ dist y z ≤ ε- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Dist.diststatement and proof · cited by 1,539
- add_commproof · cited by 1,535
- dist_commproof · cited by 188
- exists_dist_le_ltproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- disjoint_ball_closedBall_iffproof · cited by 1