Theorems · Theorem · global analysis
UniqueDiffWithinAt.mono
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Semiring 𝕜] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] {s t : Set E} {x : E}, UniqueDiffWithinAt 𝕜 s x → s ⊆ t → UniqueDiffWithinAt 𝕜 t x- Cited by
- 8 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coeproof · cited by 8,199
- Submodule.spanproof · cited by 1,504
- Denseproof · cited by 359
- UniqueDiffWithinAtstatement and proof · cited by 252
- closure_monoproof · cited by 133
- Submodule.span_monoproof · cited by 85
- tangentConeAtproof · cited by 54
Cited by8
Results whose statement or proof uses this declaration.
- UniqueMDiffWithinAt.prodproof · cited by 2
- UniqueMDiffWithinAt.image_denseRangeproof · cited by 2
- UniqueDiffWithinAt.mono_closureproof · cited by 1
- UniqueMDiffWithinAt.monoproof · cited by 1
- UniqueDiffWithinAt.closureproof · cited by 0
- uniqueDiffWithinAt_Iciproof · cited by 0
- uniqueDiffWithinAt_Iicproof · cited by 0
- UniqueMDiffOn.uniqueDiffWithinAt_range_interproof · cited by 0