Theorems · Theorem · order theory
RelEmbedding.map_rel_iff
∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : β → β → Prop} (f : r ↪r s) {a b : α}, s (f a) (f b) ↔ r a b- Defined in
- Mathlib.Order.RelIso.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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 and proof · cited by 281
- RelEmbedding.map_rel_iff'proof · cited by 3
Cited by27
Results whose statement or proof uses this declaration.
- OrderEmbedding.le_iff_leproof · cited by 32
- OrderEmbedding.lt_iff_ltproof · cited by 23
- SimpleGraph.Embedding.map_adj_iffproof · cited by 6
- IsChain.preimage_relEmbeddingproof · cited by 5
- IsAntichain.preimage_relEmbeddingproof · cited by 4
- RelIso.ofSurjectiveproof · cited by 4
- IsAntichain.image_relEmbeddingproof · cited by 4
- RelEmbedding.swapproof · cited by 3
- Ordinal.typein_lt_typeinproof · cited by 3
- BddBelow.wellFoundedOn_ltproof · cited by 3
- RelEmbedding.accproof · cited by 3
- wellFoundedGT_iff_monotone_chain_condition'proof · cited by 3