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Theorems · Theorem · real analysis

contDiffOn_univ

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {n : WithTop ℕ∞}, ContDiffOn 𝕜 n f Set.univ ↔ ContDiff 𝕜 n f
Defined in
Mathlib.Analysis.Calculus.ContDiff.Defs
Cited by
25 results in Mathlib
Foundations
Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContDiff.comp · cited by 48ContDiff.compContDiff.contDiffOn · cited by 38ContDiff.contDiffOnContDiff.comp_contDiffOn · cited by 20ContDiff.comp_contDiffOnContDiff.of_le · cited by 18ContDiff.of_leContDiff.differentiable · cited by 15ContDiff.differentiableFunction.HasTemperateGrowth.comp · cited by 12HasTemperateGrowth.compContDiff.prodMk · cited by 11ContDiff.prodMkcontDiff_zero · cited by 9contDiff_zerocontMDiff_iff_contDiff · cited by 6contMDiff_iff_contDiffcontDiff_iff_continuous_differentiable · cited by 6contDiff_iff_continuous_d…AnalyticOn.contDiff · cited by 2AnalyticOn.contDiffContDiff.fun_comp_contDiffOn · cited by 2ContDiff.fun_comp_contDif…ContDiffOn.comp_contDiff · cited by 1ContDiffOn.comp_contDiffContDiff.differentiable_one · cited by 1ContDiff.differentiable_o…iteratedDeriv_comp_const_smul · cited by 1iteratedDeriv_comp_const_…NormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceTop.top · cited by 9680Top.topNontriviallyNormedField · cited by 8742NontriviallyNormedFieldENat · cited by 4985ENatSet.univ · cited by 3945Set.univWithTop · cited by 3754WithTopnhdsWithin · cited by 1912nhdsWithinWithTop.some · cited by 1128WithTop.someFormalMultilinearSeries · cited by 615FormalMultilinearSeriesle_top · cited by 411le_topContDiff · cited by 352ContDiffContDiffOn · cited by 294ContDiffOnAnalyticOnNhd · cited by 206AnalyticOnNhduniqueDiffOn_univ · cited by 66uniqueDiffOn_univcontDiffOn_univCITED BYCITES

Cites26

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Cited by25

Results whose statement or proof uses this declaration.