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leanprover-community-mathlib4-bot committed Dec 23, 2024
2 parents a1bda00 + 85bb89c commit 88ce072
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6 changes: 6 additions & 0 deletions Mathlib/ModelTheory/Semantics.lean
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Expand Up @@ -568,6 +568,12 @@ theorem realize_graph {f : L.Functions n} {x : Fin n → M} {y : M} :
simp only [Formula.graph, Term.realize, realize_equal, Fin.cons_zero, Fin.cons_succ]
rw [eq_comm]

theorem boundedFormula_realize_eq_realize (φ : L.Formula α) (x : α → M) (y : Fin 0 → M) :
BoundedFormula.Realize φ x y ↔ φ.Realize x := by
rw [Formula.Realize, iff_iff_eq]
congr
ext i; exact Fin.elim0 i

end Formula

@[simp]
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2 changes: 1 addition & 1 deletion lake-manifest.json
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Expand Up @@ -65,7 +65,7 @@
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