Theorems · Theorem · logic and foundations
FirstOrder.Language.Embedding.injective
∀ {L : FirstOrder.Language} {M : Type w} {N : Type w'} [inst : L.Structure M] [inst_1 : L.Structure N]
(f : L.Embedding M N), Function.Injective ⇑f- Defined in
- Mathlib.ModelTheory.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
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
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Embeddingstatement and proof · cited by 128
- Function.Embedding.injectiveproof · cited by 111
- FirstOrder.Language.Embedding.toEmbeddingproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- FirstOrder.Language.DirectLimit.equiv_iffproof · cited by 3
- FirstOrder.Language.PartialEquiv.toEquiv_inclusion_applyproof · cited by 2
- FirstOrder.Language.Substructure.CG.of_map_embeddingproof · cited by 1
- FirstOrder.Language.Embedding.comp_injectiveproof · cited by 1
- FirstOrder.Language.Embedding.toHom_comp_injectiveproof · cited by 1
- FirstOrder.Language.Substructure.FG.of_map_embeddingproof · cited by 1