Mathlib Map

Theorems · Theorem · logic and foundations

FirstOrder.Language.Embedding.subtype_equivRange

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N]
  (f : L.Embedding M N), f.toHom.range.subtype.comp f.equivRange.toEmbedding = f
Defined in
Mathlib.ModelTheory.Substructures
Cited by
2 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Structure
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Language.isUltrahomogeneous_iff_IsExtensionPair · cited by 1Language.isUltrahomogeneo…FirstOrder.Language.isExtensionPair_iff_exists_embedding_closure_singleton_sup · cited by 1Language.isExtensionPair_…DFunLike.coe · cited by 62936DFunLike.coeFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Substructure · cited by 242Language.SubstructureFirstOrder.Language.Embedding · cited by 128Language.EmbeddingFirstOrder.Language.Embedding.toHom · cited by 40Embedding.toHomFirstOrder.Language.Substructure.subtype · cited by 40Substructure.subtypeFirstOrder.Language.Embedding.comp · cited by 38Embedding.compFirstOrder.Language.Equiv.toEmbedding · cited by 34Equiv.toEmbeddingFirstOrder.Language.Hom.range · cited by 30Hom.rangeFirstOrder.Language.Embedding.ext · cited by 20Embedding.extFirstOrder.Language.Embedding.equivRange · cited by 14Embedding.equivRangeEmbedding.subtype_equivRangeCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.