Theorems · Theorem · global analysis
ExistsContDiffBumpBase.y_pos_of_mem_ball
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : FiniteDimensional ℝ E]
[inst_3 : MeasurableSpace E] [inst_4 : BorelSpace E] {D : ℝ} {x : E},
0 < D → D < 1 → x ∈ Metric.ball 0 (1 + D) → 0 < ExistsContDiffBumpBase.y D x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 280 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites70
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- Norm.normproof · cited by 5,413
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Continuousproof · cited by 2,592
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
Cited by1
Results whose statement or proof uses this declaration.
- ExistsContDiffBumpBase.y_supportproof · cited by 0