Theorems · Definition · logic and foundations
FirstOrder.Language.Term.realize
{L : FirstOrder.Language} → {M : Type w} → [L.Structure M] → {α : Type u'} → (α → M) → L.Term α → MA term t with variables indexed by α can be evaluated by giving a value to each variable.
- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 81 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Termstatement and proof · cited by 166
- FirstOrder.Language.Term.brecOnproof · cited by 1
Cited by82
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Term.realize_relabelstatement and proof · cited by 15
- Set.TermDefinableproof · cited by 12
- FirstOrder.Language.BoundedFormula.realize_rel₂statement and proof · cited by 6
- FirstOrder.Language.Term.realize_constantsstatement · cited by 6
- FirstOrder.Ring.realize_termOfFreeCommRingstatement and proof · cited by 5
- FirstOrder.Ring.realize_zerostatement · cited by 5
- FirstOrder.Language.HomClass.realize_termstatement and proof · cited by 5
- FirstOrder.Language.BoundedFormula.realize_mapTermRel_idstatement and proof · cited by 4
- FirstOrder.Language.BoundedFormula.realize_restrictFreeVarproof · cited by 4
- FirstOrder.Language.BoundedFormula.realize_relstatement · cited by 3
- FirstOrder.Language.BoundedFormula.realize_relabelproof · cited by 3
- FirstOrder.Language.Substructure.coe_closure_eq_range_term_realizestatement and proof · cited by 3