Theorems · Theorem · dynamical systems
CircleDeg1Lift.commute_add_int
∀ (f : CircleDeg1Lift) (n : ℤ), Function.Commute ⇑f fun x => x + ↑n
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 113 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.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Nat.cast_oneproof · cited by 2,501
- sub_eq_add_negproof · cited by 1,023
- Nat.cast_addproof · cited by 586
- neg_add_revproof · cited by 236
- CircleDeg1Liftstatement and proof · cited by 128
- Function.Commutestatement and proof · cited by 54
- Int.cast_negSuccproof · cited by 32
- CircleDeg1Lift.commute_add_natproof · cited by 2
- CircleDeg1Lift.commute_sub_natproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- CircleDeg1Lift.map_add_intproof · cited by 2
- CircleDeg1Lift.le_iterate_of_add_int_le_mapproof · cited by 2
- CircleDeg1Lift.iterate_le_of_map_le_add_intproof · cited by 1
- CircleDeg1Lift.iterate_pos_le_iffproof · cited by 1
- CircleDeg1Lift.iterate_pos_lt_iffproof · cited by 1
- CircleDeg1Lift.commute_int_addproof · cited by 1
- CircleDeg1Lift.commute_sub_intproof · cited by 1
- CircleDeg1Lift.iterate_eq_of_map_eq_add_intproof · cited by 0
- CircleDeg1Lift.iterate_pos_eq_iffproof · cited by 0