Theorems · Theorem · functional analysis
exists_dist_lt_lt
∀ {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
- 3 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- LT.lt.leproof · cited by 2,189
- Dist.diststatement and proof · cited by 1,539
- LT.lt.ne'proof · cited by 1,417
- div_selfproof · cited by 237
- add_nonnegproof · cited by 104
- div_nonnegproof · cited by 103
- add_divproof · cited by 89
- div_lt_oneproof · cited by 38
- add_posproof · cited by 28
Cited by3
Results whose statement or proof uses this declaration.
- infEDist_thickeningproof · cited by 3
- thickening_thickeningproof · cited by 2
- disjoint_ball_ball_iffproof · cited by 0