Theorems · Theorem · real analysis
variationOnFromTo.eq_of_le
∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] (f : α → E) (s : Set α)
{a b : α}, a ≤ b → variationOnFromTo f s a b = (eVariationOn f (s ∩ Set.Icc a b)).toReal- Cited by
- 8 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 25,697
- LinearOrderstatement and proof · cited by 8,572
- Set.Iccstatement · cited by 1,702
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.toRealstatement · cited by 859
- eVariationOnstatement · cited by 90
- variationOnFromTostatement · cited by 33
Cited by8
Results whose statement or proof uses this declaration.
- variationOnFromTo.addproof · cited by 10
- variationOnFromTo.eq_of_geproof · cited by 3
- variationOnFromTo.abs_sub_le_sub_of_leproof · cited by 2
- hasConstantSpeedOnWith_iff_variationOnFromTo_eqproof · cited by 1
- variationOnFromTo.comp_eq_of_monotoneOnproof · cited by 1
- variationOnFromTo.edist_zero_of_eq_zeroproof · cited by 1
- variationOnFromTo.eq_zero_iff_of_leproof · cited by 1
- has_unit_speed_naturalParameterizationproof · cited by 0