Theorems · Theorem · real analysis
contDiff_id
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {n : WithTop ℕ∞}, ContDiff 𝕜 n idThe identity is C^n.
- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Basic
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- ContDiffstatement · cited by 352
- IsBoundedLinearMap.contDiffproof · cited by 6
- IsBoundedLinearMap.idproof · cited by 2
Cited by40
Results whose statement or proof uses this declaration.
- contDiffAt_idproof · cited by 16
- contDiffOn_idproof · cited by 14
- contDiffWithinAt_idproof · cited by 12
- Complex.contDiff_cosproof · cited by 9
- Complex.contDiff_sinproof · cited by 9
- contDiffWithinAtProp_idproof · cited by 5
- contDiff_norm_sqproof · cited by 5
- AffineMap.contDiff_lineMap_uncurryproof · cited by 5
- ContDiffWithinAt.powproof · cited by 4
- ContDiffBump.contDiffproof · cited by 4
- contMDiffOn_projIccproof · cited by 4
- Real.smoothTransition.contDiffproof · cited by 3