Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.iSup_eq_closure
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {ι : Sort u_3} (S : ι → L.Substructure M),
⨆ i, S i = (FirstOrder.Language.Substructure.closure L).toFun (⋃ i, ↑(S i))- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.iUnionstatement · cited by 2,483
- iSupstatement and proof · cited by 2,415
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- LowerAdjoint.toFunstatement · cited by 105
- FirstOrder.Language.Substructure.closurestatement · cited by 70
- FirstOrder.Language.Substructure.closure_eqproof · cited by 7
- FirstOrder.Language.Substructure.closure_iUnionproof · cited by 3
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