Theorems · Inductive type · global analysis
ContDiffBump
{E : Type u_1} → E → Typef : ContDiffBump c, where c is a point in a normed vector space, is a
bundled smooth function such that
- f is equal to 1 in Metric.closedBall c f.rIn;
- support f = Metric.ball c f.rOut;
- 0 ≤ f x ≤ 1 for all x.
The structure ContDiffBump contains the data required to construct the function:
real numbers rIn, rOut, and proofs of 0 < rIn < rOut. The function itself is available through
CoeFun when the space is nice enough, i.e., satisfies the HasContDiffBump typeclass.
- Cited by
- 61 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by77
Results whose statement or proof uses this declaration.
- ContDiffBump.rOutstatement and proof · cited by 51
- ContDiffBump.toFunstatement and proof · cited by 43
- SmoothBumpFunction.toContDiffBumpstatement · cited by 27
- ContDiffBump.normedstatement and proof · cited by 22
- ContDiffBump.rInstatement and proof · cited by 22
- ContDiffBump.rIn_posstatement and proof · cited by 10
- ContDiffBump.rOut_posstatement and proof · cited by 9
- ContDiffBump.support_eqstatement and proof · cited by 8
- ContDiffBump.nonnegstatement and proof · cited by 6
- ContDiffBump.le_onestatement and proof · cited by 5
- ContDiffBump.support_normed_eqstatement and proof · cited by 5
- ContDiffBump.contDiffstatement and proof · cited by 4