Theorems · Theorem · global analysis
range_mfderiv_coe_sphere
Deprecated since 2026-08-02Use range_mvfderiv_subtypeVal instead.
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] {n : ℕ}
[inst_2 : Fact (Module.finrank ℝ E = n + 1)] (v : ↑(Metric.sphere 0 1)), (↑(mfderiv% Subtype.val v)).range = (ℝ ∙ ↑v)ᗮ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 249 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- ENNRealstatement · cited by 9,879
- Submodulestatement · cited by 7,192
- Set.Elemstatement and proof · cited by 7,166
- InnerProductSpacestatement and proof · cited by 3,523
- Factstatement and proof · cited by 2,726
- Module.finrankstatement and proof · cited by 1,770
- Submodule.spanstatement and proof · cited by 1,504
- modelWithCornersSelfstatement and proof · cited by 920
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.