Theorems · Theorem · dynamical systems
Function.IsFixedPt.left_of_comp
∀ {α : Type u_1} {f g : α → α} {x : α}, Function.IsFixedPt (f ∘ g) x → Function.IsFixedPt g x → Function.IsFixedPt f xIf x is a fixed point of f ∘ g and g, then it is a fixed point of f.
- Defined in
- Mathlib.Dynamics.FixedPoints.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Function.IsFixedPtstatement and proof · cited by 84
Cited by2
Results whose statement or proof uses this declaration.
- Function.IsPeriodicPt.left_of_addproof · cited by 2
- Function.IsPeriodicPt.left_of_compproof · cited by 1