Theorems · Theorem · logic and foundations
FirstOrder.Language.LHom.mem_substructureReduct
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {L' : FirstOrder.Language} [inst_1 : L'.Structure M]
(φ : L →ᴸ L') [inst_2 : φ.IsExpansionOn M] {x : M} {S : L'.Substructure M}, x ∈ φ.substructureReduct S ↔ x ∈ S- Defined in
- Mathlib.ModelTheory.Substructures
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- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
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- DFunLike.coestatement · cited by 62,936
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- OrderEmbeddingstatement · cited by 619
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- FirstOrder.Language.LHomstatement and proof · cited by 66
- FirstOrder.Language.LHom.IsExpansionOnstatement and proof · cited by 31
- FirstOrder.Language.LHom.substructureReductstatement · cited by 6
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