Theorems · Theorem · global analysis
ContDiffBump.pos_of_mem_ball
∀ {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.ball c f.rOut → 0 < ↑f x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · 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
- Metric.ballstatement and proof · cited by 735
- ContDiffBumpstatement and proof · cited by 61
- Function.mem_supportproof · cited by 54
- ContDiffBump.rOutstatement and proof · cited by 51
- HasContDiffBumpstatement and proof · cited by 46
- ContDiffBump.toFunstatement · cited by 43
- LE.le.lt_of_ne'proof · cited by 41
- ContDiffBump.support_eqproof · cited by 8
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