Theorems · Theorem · global analysis
ContDiffBump.zero_of_le_dist
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : HasContDiffBump E] {c : E}
(f : ContDiffBump c) {x : E}, f.rOut ≤ dist x c → ↑f x = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · 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
- Dist.diststatement and proof · cited by 1,539
- not_ltproof · cited by 306
- ContDiffBumpstatement and proof · cited by 61
- ContDiffBump.rOutstatement and proof · cited by 51
- Metric.mem_ballproof · cited by 47
- HasContDiffBumpstatement and proof · cited by 46
- ContDiffBump.toFunstatement · cited by 43
- Function.notMem_supportproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- ContDiffBump.integral_le_measure_closedBallproof · cited by 0