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Theorems · Theorem · logic and foundations

FirstOrder.Language.Embedding.ext

∀ {L : FirstOrder.Language} {M : Type w} {N : Type w'} [inst : L.Structure M] [inst_1 : L.Structure N]
  ⦃f g : L.Embedding M N⦄, (∀ (x : M), f x = g x) → f = g
Defined in
Mathlib.ModelTheory.Basic
Cited by
20 results in Mathlib
Foundations
Depth 16 from the axioms · uses Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Structure

Around this declaration

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

FirstOrder.Language.PartialEquiv.ext · cited by 3PartialEquiv.extFirstOrder.Language.Embedding.subtype_equivRange · cited by 2Embedding.subtype_equivRa…FirstOrder.Language.Embedding.toHom_injective · cited by 2Embedding.toHom_injectiveFirstOrder.Language.IsUltrahomogeneous.extend_embedding · cited by 2IsUltrahomogeneous.extend…FirstOrder.Language.PartialEquiv.le_iff · cited by 1PartialEquiv.le_iffFirstOrder.Language.empty.isFraisseLimit_of_countable_infinite · cited by 1empty.isFraisseLimit_of_c…FirstOrder.Language.DirectLimit.Equiv_isup_symm_inclusion · cited by 1DirectLimit.Equiv_isup_sy…FirstOrder.Language.isExtensionPair_iff_exists_embedding_closure_singleton_sup · cited by 1Language.isExtensionPair_…FirstOrder.Language.isUltrahomogeneous_iff_IsExtensionPair · cited by 1Language.isUltrahomogeneo…FirstOrder.Language.dlo_isExtensionPair · cited by 1Language.dlo_isExtensionP…FirstOrder.Language.IsFraisseLimit.isExtensionPair · cited by 1IsFraisseLimit.isExtensio…FirstOrder.Language.Embedding.comp_injective · cited by 1Embedding.comp_injectiveFirstOrder.Language.Embedding.ext_iff · cited by 1Embedding.ext_iffFirstOrder.Language.IsUltrahomogeneous.amalgamation_age · cited by 1IsUltrahomogeneous.amalga…FirstOrder.Language.Embedding.subtype_comp_codRestrict · cited by 0Embedding.subtype_comp_co…DFunLike.coe · cited by 62936DFunLike.coeFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Embedding · cited by 128Language.EmbeddingFirstOrder.Language.Embedding.coe_injective · cited by 1Embedding.coe_injectiveEmbedding.extCITED BYCITES

Cites5

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Cited by20

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