Theorems · Theorem · global analysis
ContDiffBump.one_of_mem_closedBall
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : HasContDiffBump E] {c : E}
(f : ContDiffBump c) {x : E}, x ∈ Metric.closedBall c f.rIn → ↑f x = 1- Cited by
- 4 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- NormedSpacestatement and proof · cited by 12,499
- Norm.normproof · cited by 5,413
- LT.lt.leproof · cited by 2,189
- Metric.closedBallstatement and proof · cited by 704
- abs_of_nonnegproof · cited by 279
- norm_smulproof · cited by 242
- ContDiffBumpstatement and proof · cited by 61
- ContDiffBump.rOutproof · cited by 51
- HasContDiffBumpstatement and proof · cited by 46
Cited by4
Results whose statement or proof uses this declaration.
- exists_contDiff_tsupport_subsetproof · cited by 3
- ContDiffBump.measure_closedBall_le_integralproof · cited by 2
- ContDiffBump.eventuallyEq_one_of_mem_ballproof · cited by 1
- SmoothBumpFunction.one_of_dist_leproof · cited by 1