Theorems · Definition
Function.IsFixedPt
{α : Type u₁} → (α → α) → α → PropA point x is a fixed point of f : α → α if f x = x.
- Defined in
- Mathlib.Logic.Function.Defs
- Cited by
- 84 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by86
Results whose statement or proof uses this declaration.
- Function.fixedPointsproof · cited by 90
- Function.IsPeriodicPtproof · cited by 68
- Function.IsFixedPt.eqstatement and proof · cited by 14
- Function.IsFixedPt.iteratestatement and proof · cited by 9
- Function.IsPeriodicPt.mul_constproof · cited by 6
- Function.isFixedPt_idstatement · cited by 5
- Function.minimalPeriod_eq_one_iff_isFixedPtstatement and proof · cited by 5
- ContractingWith.exists_fixedPointstatement and proof · cited by 4
- ContractingWith.exists_fixedPoint'statement and proof · cited by 4
- ContractingWith.fixedPoint_isFixedPtstatement · cited by 4
- Equiv.Perm.card_fixedPointsproof · cited by 4
- Function.IsFixedPt.perm_zpowstatement and proof · cited by 4