Theorems · Theorem · real analysis
variationOnFromTo.eq_neg_swap
∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] (f : α → E) (s : Set α)
(a b : α), variationOnFromTo f s a b = -variationOnFromTo f s b a- Cited by
- 6 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Realstatement and proof · cited by 25,697
- LinearOrderstatement and proof · cited by 8,572
- LT.lt.leproof · cited by 2,189
- Set.Iccproof · cited by 1,702
- PseudoEMetricSpacestatement and proof · cited by 1,536
- neg_negproof · cited by 960
- ENNReal.toRealproof · cited by 859
- neg_zeroproof · cited by 542
- LT.lt.not_geproof · cited by 305
- lt_trichotomyproof · cited by 178
- eVariationOnproof · cited by 90
Cited by6
Results whose statement or proof uses this declaration.
- variationOnFromTo.addproof · cited by 10
- variationOnFromTo.eq_of_geproof · cited by 3
- LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn'proof · cited by 1
- variationOnFromTo.edist_zero_of_eq_zeroproof · cited by 1
- variationOnFromTo.nonpos_of_geproof · cited by 0
- has_unit_speed_naturalParameterizationproof · cited by 0