Theorems · Theorem · order theory
InitialSeg.eq_principalSeg
∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder β s] (f : InitialSeg r s)
(g : PrincipalSeg r s) (a : α), g.toRelEmbedding a = f a- Defined in
- Mathlib.Order.InitialSeg
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsWellOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RelEmbeddingstatement · cited by 281
- IsWellOrderstatement and proof · cited by 171
- PrincipalSeg.toRelEmbeddingstatement and proof · cited by 129
- PrincipalSegstatement and proof · cited by 73
- InitialSegstatement and proof · cited by 70
- PrincipalSeg.mem_range_of_relproof · cited by 24
- InitialSeg.eqproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- InitialSeg.transPrincipal_applyproof · cited by 1