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Theorems · Theorem · global analysis

ContDiffBumpBase.mem_Icc

∀ {E : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (self : ContDiffBumpBase E) (R : ℝ) (x : E),
  self.toFun R x ∈ Set.Icc 0 1
Defined in
Mathlib.Analysis.Calculus.BumpFunction.Basic
Cited by
2 results in Mathlib
Foundations
Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContDiffBump.nonneg · cited by 6ContDiffBump.nonnegContDiffBump.le_one · cited by 5ContDiffBump.le_oneSet · cited by 53352SetReal · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceSet.Icc · cited by 1702Set.IccContDiffBumpBase · cited by 11ContDiffBumpBaseContDiffBumpBase.toFun · cited by 7ContDiffBumpBase.toFunContDiffBumpBase.mem_IccCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.