Theorems · Theorem · dynamical systems
CircleDeg1Lift.translationNumber_le_of_le_add_int
∀ (f : CircleDeg1Lift) {x : ℝ} {m : ℤ}, f x ≤ x + ↑m → f.translationNumber ≤ ↑m- Cited by
- 4 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Realstatement and proof · cited by 25,697
- CircleDeg1Liftstatement and proof · cited by 128
- Nat.cast_add_oneproof · cited by 56
- CircleDeg1Lift.translationNumberstatement · cited by 48
- sub_le_iff_le_add'proof · cited by 41
- div_le_iff₀'proof · cited by 28
- le_of_tendsto'proof · cited by 25
- Nat.cast_add_one_posproof · cited by 18
- CircleDeg1Lift.coe_powproof · cited by 6
- CircleDeg1Lift.tendsto_translation_number'proof · cited by 2
- CircleDeg1Lift.iterate_le_of_map_le_add_intproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- CircleDeg1Lift.translationNumber_of_eq_add_intproof · cited by 2
- CircleDeg1Lift.lt_map_of_int_lt_translationNumberproof · cited by 1
- CircleDeg1Lift.translationNumber_le_of_le_add_natproof · cited by 0
- CircleDeg1Lift.translationNumber_le_ceil_subproof · cited by 0