Theorems · Definition · logic and foundations
FirstOrder.Language.Equiv.toEmbedding
{L : FirstOrder.Language} →
{M : Type w} → {N : Type w'} → [inst : L.Structure M] → [inst_1 : L.Structure N] → L.Equiv M N → L.Embedding M NA first-order equivalence is also a first-order embedding.
- Defined in
- Mathlib.ModelTheory.Basic
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
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
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Embeddingstatement · cited by 128
- FirstOrder.Language.Equivstatement · cited by 83
- FirstOrder.Language.StrongHomClass.toEmbeddingproof · cited by 4
Cited by39
Results whose statement or proof uses this declaration.
- FirstOrder.Language.PartialEquiv.dom_le_domproof · cited by 8
- FirstOrder.Language.PartialEquiv.cod_le_codproof · cited by 6
- FirstOrder.Language.IsUltrahomogeneousproof · cited by 5
- FirstOrder.Language.PartialEquiv.toEmbeddingOfEqTopproof · cited by 5
- FirstOrder.Language.PartialEquiv.subtype_toEquiv_inclusionstatement and proof · cited by 3
- FirstOrder.Language.DirectLimit.equiv_liftproof · cited by 3
- FirstOrder.Language.PartialEquiv.le_defstatement · cited by 2
- FirstOrder.Language.Embedding.subtype_equivRangestatement and proof · cited by 2
- FirstOrder.Language.PartialEquiv.toEmbeddingproof · cited by 2
- FirstOrder.Language.Equiv.comp_toEmbeddingstatement · cited by 2
- FirstOrder.Language.age.jointEmbeddingproof · cited by 2
- FirstOrder.Language.Equiv.refl_toEmbeddingstatement · cited by 2