Theorems · Theorem · functional analysis
ContDiffMapSupportedIn.structureMapCLM_apply
∀ (𝕜 : Type u_1) {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace ℝ E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace ℝ F] [inst_5 : NormedSpace 𝕜 F]
[inst_6 : SMulCommClass ℝ 𝕜 F] {n : ℕ∞} {K : TopologicalSpace.Compacts E} {i : ℕ}
(f : ContDiffMapSupportedIn E F n K),
⇑((ContDiffMapSupportedIn.structureMapCLM 𝕜 n i) f) = if ↑i ≤ n then iteratedFDeriv ℝ i ⇑f else 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement · cited by 5,352
- ENatstatement and proof · cited by 4,985
- SMulCommClassstatement and proof · cited by 1,927
- ContinuousMultilinearMapstatement · cited by 1,016
- BoundedContinuousFunctionstatement · cited by 511
- TopologicalSpace.Compactsstatement and proof · cited by 386
Cited by6
Results whose statement or proof uses this declaration.
- ContDiffMapSupportedIn.seminorm_le_iffproof · cited by 3
- ContDiffMapSupportedIn.seminorm_eq_bot_of_gtproof · cited by 1
- ContDiffMapSupportedIn.continuous_iff_comp_order_leproof · cited by 0
- ContDiffMapSupportedIn.seminorm_fderivLM_topproof · cited by 0
- ContDiffMapSupportedIn.seminorm_monoLM_eqproof · cited by 0
- ContDiffMapSupportedIn.norm_toBoundedContinuousFunctionproof · cited by 0