Theorems · Theorem · real analysis
variationOnFromTo.eq_of_ge
∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] (f : α → E) (s : Set α)
{a b : α}, b ≤ a → variationOnFromTo f s a b = -(eVariationOn f (s ∩ Set.Icc b a)).toReal- Cited by
- 3 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.Iccstatement and proof · cited by 1,702
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.toRealstatement and proof · cited by 859
- eVariationOnstatement and proof · cited by 90
- neg_injproof · cited by 85
- variationOnFromTostatement · cited by 33
- variationOnFromTo.eq_of_leproof · cited by 8
- variationOnFromTo.eq_neg_swapproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- variationOnFromTo.eq_zero_iff_of_geproof · cited by 1
- hasConstantSpeedOnWith_iff_variationOnFromTo_eqproof · cited by 1
- variationOnFromTo.comp_eq_of_monotoneOnproof · cited by 1