Theorems · Theorem · order theory
Order.height_le_height_apply_of_strictMono
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (f : α → β),
StrictMono f → ∀ (x : α), Order.height x ≤ Order.height (f x)- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- ENatstatement · cited by 4,985
- iSupproof · cited by 2,415
- StrictMonostatement and proof · cited by 706
- iSup_congr_Propproof · cited by 247
- RelSeries.lengthproof · cited by 195
- RelSeries.lastproof · cited by 114
- iSup₂_leproof · cited by 96
- LTSeriesproof · cited by 87
- Order.heightstatement · cited by 67
- le_iSup₂_of_leproof · cited by 52
- LTSeries.mapproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- Order.height_orderIsoproof · cited by 1
- Order.coheight_le_coheight_apply_of_strictMonoproof · cited by 1