Theorems · Theorem · real analysis
eVariationOn.constant_on
∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {f : α → E} {s : Set α},
(f '' s).Subsingleton → eVariationOn f s = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- ENNRealstatement and proof · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- Set.imagestatement and proof · cited by 5,609
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.edistproof · cited by 735
- Set.Subsingletonstatement and proof · cited by 276
- eVariationOnstatement · cited by 90
- PseudoEMetricSpace.edist_selfproof · cited by 50
- eVariationOn.eq_zero_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- eVariationOn.subsingletonproof · cited by 22