Theorems · Theorem · logic and foundations
FirstOrder.Language.Term.realize_mem
∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {S : L.Substructure M} {α : Type u_3} (t : L.Term α)
(xs : α → M), (∀ (a : α), xs a ∈ S) → FirstOrder.Language.Term.realize xs t ∈ S- Defined in
- Mathlib.ModelTheory.Substructures
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- FirstOrder.Language.Term.realizestatement and proof · cited by 81
- FirstOrder.Language.Substructure.fun_memproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Substructure.coe_closure_eq_range_term_realizeproof · cited by 3