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Theorems · Theorem · global analysis

ExistsContDiffBumpBase.u_nonneg

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : FiniteDimensional ℝ E] (x : E),
  0 ≤ ExistsContDiffBumpBase.u x
Defined in
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension
Cited by
2 results in Mathlib
Foundations
Depth 236 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpaceFiniteDimensional
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Around this declaration

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

ExistsContDiffBumpBase.u_int_pos · cited by 4ExistsContDiffBumpBase.u_…ExistsContDiffBumpBase.w_nonneg · cited by 2ExistsContDiffBumpBase.w_…Real · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceFiniteDimensional · cited by 1854FiniteDimensionalExistsContDiffBumpBase.u · cited by 14ExistsContDiffBumpBase.uExistsContDiffBumpBase.u_exists · cited by 5ExistsContDiffBumpBase.u_…ExistsContDiffBumpBase.u_nonn…CITED BYCITES

Cites6

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.