Theorems · Definition · logic and foundations
FirstOrder.Language.Embedding.refl
(L : FirstOrder.Language) → (M : Type w) → [inst : L.Structure M] → L.Embedding M M
The identity embedding from a structure to itself.
- Defined in
- Mathlib.ModelTheory.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement and proof · cited by 1,084
- Function.Embeddingproof · cited by 988
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Embeddingstatement · cited by 128
- Function.Embedding.reflproof · cited by 29
Cited by11
Results whose statement or proof uses this declaration.
- FirstOrder.Language.DirectedSystem.natLERecproof · cited by 3
- FirstOrder.Language.Equiv.refl_toEmbeddingstatement · cited by 2
- FirstOrder.Language.exists_cg_is_age_ofproof · cited by 1
- FirstOrder.Language.Embedding.refl_applystatement · cited by 0
- FirstOrder.Language.Embedding.refl_compstatement and proof · cited by 0
- FirstOrder.Language.Embedding.comp_reflstatement and proof · cited by 0
- FirstOrder.Language.Embedding.refl_toHomstatement · cited by 0
- FirstOrder.Language.Equiv.self_comp_symm_toEmbeddingstatement and proof · cited by 0
- FirstOrder.Language.Substructure.inclusion_selfstatement · cited by 0
- FirstOrder.Language.Equiv.symm_comp_self_toEmbeddingstatement and proof · cited by 0
- FirstOrder.Language.DirectedSystem.coe_natLERecproof · cited by 0