Theorems · Theorem · real analysis

differentiable_of_subsingleton

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [inst_3 : TopologicalSpace E] {F : Type u_3} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜 F]
  [inst_6 : TopologicalSpace F] [Subsingleton E] {f : E → F}, Differentiable 𝕜 f

Defined in: Mathlib.Analysis.Calculus.FDeriv.Const
Cited by: 1 results in Mathlib
Foundations: Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField AddCommGroup Module TopologicalSpace AddCommGroup Module TopologicalSpace Subsingleton

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

TopologicalSpacestatement and proof · cited by 24,529
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
NontriviallyNormedFieldstatement and proof · cited by 8,742
Differentiablestatement · cited by 298
HasFDerivAt.differentiableAtproof · cited by 83
hasFDerivAt_of_subsingletonproof · cited by 6

Cited by1

Results whose statement or proof uses this declaration.

differentiableWithinAt_of_subsingletonproof · cited by 0