Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.notMem_of_notMem_closure
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {s : Set M} {P : M},
P ∉ (FirstOrder.Language.Substructure.closure L).toFun s → P ∉ s- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement · cited by 8,199
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement · cited by 242
- LowerAdjoint.toFunstatement and proof · cited by 105
- FirstOrder.Language.Substructure.closurestatement and proof · cited by 70
- FirstOrder.Language.Substructure.subset_closureproof · cited by 12
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