Theorems · Theorem · order theory
StrictMono.le_apply
∀ {β : Type u_2} [inst : LinearOrder β] [WellFoundedLT β] {f : β → β}, StrictMono f → ∀ {x : β}, x ≤ f x- Defined in
- Mathlib.Order.WellFounded
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderWellFoundedLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- WellFoundedLTstatement and proof · cited by 491
- StrictMono.id_leproof · cited by 14
Cited by32
Results whose statement or proof uses this declaration.
- Ordinal.right_le_opowproof · cited by 4
- Ordinal.nfpFamily_fpproof · cited by 4
- Ordinal.right_le_veblenWithproof · cited by 3
- IsAdicComplete.StrictMono.mk_liftRingHomproof · cited by 3
- Cardinal.IsInaccessible.preAleph_ordproof · cited by 3
- Cardinal.IsInaccessible.preBeth_ordproof · cited by 3
- Ordinal.op_eq_self_of_isPrincipalproof · cited by 3
- Ordinal.mem_range_derivproof · cited by 2
- Order.IsNormal.dirSupClosed_rangeproof · cited by 2
- Ordinal.fp_iff_derivFamilyproof · cited by 2
- StrictMono.not_bddAbove_range_of_wellFoundedLTproof · cited by 2
- Order.IsNormal.le_iff_le_sSup'proof · cited by 2