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
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.
- DFunLike.coestatement and proof · 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
- FirstOrder.Language.Embedding.coe_injectiveproof · cited by 1
Cited by20
Results whose statement or proof uses this declaration.
- FirstOrder.Language.PartialEquiv.extproof · cited by 3
- FirstOrder.Language.Embedding.subtype_equivRangeproof · cited by 2
- FirstOrder.Language.Embedding.toHom_injectiveproof · cited by 2
- FirstOrder.Language.IsUltrahomogeneous.extend_embeddingproof · cited by 2
- FirstOrder.Language.PartialEquiv.le_iffproof · cited by 1
- FirstOrder.Language.empty.isFraisseLimit_of_countable_infiniteproof · cited by 1
- FirstOrder.Language.DirectLimit.Equiv_isup_symm_inclusionproof · cited by 1
- FirstOrder.Language.isUltrahomogeneous_iff_IsExtensionPairproof · cited by 1
- FirstOrder.Language.dlo_isExtensionPairproof · cited by 1
- FirstOrder.Language.IsFraisseLimit.isExtensionPairproof · cited by 1
- FirstOrder.Language.Embedding.comp_injectiveproof · cited by 1