Theorems · Theorem · logic and foundations
FirstOrder.Language.Substructure.coe_closure_eq_range_term_realize
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {s : Set M},
↑((FirstOrder.Language.Substructure.closure L).toFun s) = Set.range (FirstOrder.Language.Term.realize Subtype.val)- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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 and proof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.rangestatement and proof · cited by 4,705
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Substructurestatement and proof · cited by 242
- FirstOrder.Language.Termstatement and proof · cited by 166
- FirstOrder.Language.Functionsproof · cited by 153
- LowerAdjoint.toFunstatement · cited by 105
- FirstOrder.Language.Term.realizestatement and proof · cited by 81
- SetLike.ext'_iffproof · cited by 78
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.lift_card_closure_le_card_termproof · cited by 2
- FirstOrder.Language.MeetsDefinable.closure_eq_selfproof · cited by 1
- FirstOrder.Language.Substructure.mem_closure_iff_exists_termproof · cited by 0