Theorems · Theorem · global analysis
ExistsContDiffBumpBase.u_exists
∀ (E : Type u_1) [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E],
∃ u,
ContDiff ℝ (↑⊤) u ∧ (∀ (x : E), u x ∈ Set.Icc 0 1) ∧ Function.support u = Metric.ball 0 1 ∧ ∀ (x : E), u (-x) = u x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 234 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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
- Top.topstatement and proof · cited by 9,680
- ENatstatement · cited by 4,985
- Set.rangeproof · cited by 4,705
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- IsOpenproof · cited by 2,400
- Nat.cast_zeroproof · cited by 1,870
- FiniteDimensionalstatement and proof · cited by 1,854
Cited by6
Results whose statement or proof uses this declaration.
- ExistsContDiffBumpBase.uproof · cited by 14
- ExistsContDiffBumpBase.u_supportproof · cited by 4
- ExistsContDiffBumpBase.u_nonnegproof · cited by 2
- ExistsContDiffBumpBase.u_smoothproof · cited by 2
- ExistsContDiffBumpBase.u_negproof · cited by 1
- ExistsContDiffBumpBase.u_le_oneproof · cited by 0