Theorems · Theorem · global analysis

ContDiff.dSmooth

∀ {X : Type u_1} [inst : DiffeologicalSpace X] {Y : Type u_2} [inst_1 : NormedAddCommGroup X] [inst_2 : NormedSpace ℝ X]
  [Diffeology.IsContDiffCompatible X] [inst_4 : NormedAddCommGroup Y] [inst_5 : NormedSpace ℝ Y]
  [inst_6 : DiffeologicalSpace Y] [Diffeology.IsContDiffCompatible Y] {f : X → Y},
  ContDiff ℝ (↑⊤) f → Diffeology.DSmooth f

Defined in: Mathlib.Geometry.Diffeology.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DiffeologicalSpace NormedAddCommGroup NormedSpace Diffeology.IsContDiffCompatible NormedAddCommGroup NormedSpace DiffeologicalSpace Diffeology.IsContDiffCompatible

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Cites15

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
Top.topstatement and proof · cited by 9,680
ENatstatement · cited by 4,985
WithTop.somestatement and proof · cited by 1,128
ContDiffstatement and proof · cited by 352
EuclideanSpaceproof · cited by 307
DiffeologicalSpacestatement and proof · cited by 60
ContDiff.compproof · cited by 48
Diffeology.IsPlotproof · cited by 29
Diffeology.DSmoothstatement · cited by 16

Cited by1

Results whose statement or proof uses this declaration.

Diffeology.dSmooth_iff_contDiffproof · cited by 0