Theorems · Theorem · order theory
Order.IsNormal.comp
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {f : α → β} {g : β → γ} [inst : LinearOrder α] [inst_1 : LinearOrder β]
[inst_2 : LinearOrder γ], Order.IsNormal g → Order.IsNormal f → Order.IsNormal (g ∘ f)- Defined in
- Mathlib.Order.IsNormal
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 21 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.
- LinearOrderstatement and proof · cited by 8,572
- Set.imageproof · cited by 5,609
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- Set.Iioproof · cited by 1,166
- Set.image_congrproof · cited by 533
- upperBoundsproof · cited by 263
- Order.IsSuccLimitproof · cited by 255
- Order.IsNormalstatement and proof · cited by 118
- Order.IsNormal.strictMonoproof · cited by 44
- StrictMono.compproof · cited by 36
- Order.IsNormal.le_iff_forall_leproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- Ordinal.opow_addproof · cited by 9
- Ordinal.opow_mulproof · cited by 4
- Cardinal.isNormal_alephproof · cited by 1
- Cardinal.isNormal_bethproof · cited by 1
- Ordinal.isNormal_omegaproof · cited by 1