Theorems · Theorem · order theory
StrictMono.le_id
∀ {β : Type u_2} [inst : LinearOrder β] [WellFoundedGT β] {f : β → β}, StrictMono f → f ≤ idA strictly monotone function f on a cowell-order satisfies f x ≤ x for all x.
- Defined in
- Mathlib.Order.WellFounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderWellFoundedGT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- StrictMonostatement and proof · cited by 706
- WellFoundedGTstatement and proof · cited by 114
- StrictMono.id_leproof · cited by 14
- StrictMono.dualproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- StrictMono.eq_idproof · cited by 1