Theorems · Theorem · dynamical systems
CircleDeg1Lift.forall_map_sub_of_Icc
∀ (f : CircleDeg1Lift) (P : ℝ → Prop), (∀ x ∈ Set.Icc 0 1, P (f x - x)) → ∀ (x : ℝ), P (f x - x)
If a predicate depends only on f x - x and holds for all 0 ≤ x ≤ 1,
then it holds for all x.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.Iccstatement and proof · cited by 1,702
- le_of_ltproof · cited by 1,175
- CircleDeg1Liftstatement and proof · cited by 128
- Int.fractproof · cited by 114
- Int.fract_lt_oneproof · cited by 20
- Int.fract_nonnegproof · cited by 17
- CircleDeg1Lift.map_fract_sub_fract_eqproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CircleDeg1Lift.lt_translationNumber_of_forall_add_ltproof · cited by 1
- CircleDeg1Lift.translationNumber_lt_of_forall_lt_addproof · cited by 1