Theorems · Theorem · functional analysis
ContDiff.euclidean_dist
∀ {F : Type u_2} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℝ F] {G : Type u_3} [inst_2 : NormedAddCommGroup G]
[inst_3 : NormedSpace ℝ G] [inst_4 : FiniteDimensional ℝ G] {f g : F → G} {n : ℕ∞},
ContDiff ℝ (↑n) f → ContDiff ℝ (↑n) g → (∀ (x : F), f x ≠ g x) → ContDiff ℝ ↑n fun x => Euclidean.dist (f x) (g x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENatstatement and proof · cited by 4,985
- FiniteDimensionalstatement and proof · cited by 1,854
- WithTop.somestatement and proof · cited by 1,128
- ContDiffstatement and proof · cited by 352
- ContDiff.compproof · cited by 48
- toEuclideanproof · cited by 16
- ContinuousLinearEquiv.contDiffproof · cited by 13
- ContinuousLinearEquiv.injectiveproof · cited by 11
- Euclidean.diststatement · cited by 2
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