Theorems · Theorem · order theory
InitialSeg.strictMono
∀ {α : Type u_1} {β : Type u_2} [inst : PartialOrder β] [inst_1 : PartialOrder α] (f : α ≤i β), StrictMono ⇑f- Defined in
- Mathlib.Order.InitialSeg
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- StrictMonostatement · cited by 706
- InitialSegstatement and proof · cited by 70
- OrderEmbedding.strictMonoproof · cited by 26
- InitialSeg.toOrderEmbeddingproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- InitialSeg.lt_apply_iffproof · cited by 3
- InitialSeg.isMin_apply_iffproof · cited by 2
- InitialSeg.isNormalproof · cited by 2
- PrincipalSeg.strictMonoproof · cited by 0