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ModelTheory/Arithmetic/Presburger/Semilinear Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -175,7 +175,7 @@ semilinear. -/
175175public theorem isSemilinearSet_setOf_eq [AddMonoid.FG M] {F G : Type *} [FunLike F M N]
176176 [AddMonoidHomClass F M N] [FunLike G M N] [AddMonoidHomClass G M N] (a b : N) (f : F) (g : G) :
177177 IsSemilinearSet { x | a + f x = b + g x } := by
178- rcases fg_iff_exists_fin_addMonoidHom.1 (AddMonoid.FG. fg_top (M := M)) with ⟨n, h, hh⟩
178+ rcases fg_iff_exists_fin_addMonoidHom.1 (AddMonoid.fg_top (M := M)) with ⟨n, h, hh⟩
179179 rw [AddMonoidHom.mrange_eq_top] at hh
180180 rw [← image_preimage_eq { x | a + f x = b + g x } hh, preimage_setOf_eq]
181181 apply IsSemilinearSet.image
@@ -225,7 +225,7 @@ semilinear. -/
225225public theorem IsSemilinearSet.preimage [AddMonoid.FG M] {F : Type *} [FunLike F M N]
226226 [AddMonoidHomClass F M N] {s : Set N} (hs : IsSemilinearSet s) (f : F) :
227227 IsSemilinearSet (f ⁻¹' s) := by
228- rcases fg_iff_exists_fin_addMonoidHom.1 (AddMonoid.FG. fg_top (M := M)) with ⟨n, g, hg⟩
228+ rcases fg_iff_exists_fin_addMonoidHom.1 (AddMonoid.fg_top (M := M)) with ⟨n, g, hg⟩
229229 rw [AddMonoidHom.mrange_eq_top] at hg
230230 rw [← image_preimage_eq (f ⁻¹' s) hg]
231231 apply image
Original file line number Diff line number Diff line change @@ -105,7 +105,7 @@ theorem span_invSubmonoid : Submodule.span R (invSubmonoid M S : Set S) = ⊤ :=
105105
106106theorem finiteType_of_monoid_fg [Monoid.FG M] : Algebra.FiniteType R S := by
107107 have := Monoid.fg_of_surjective _ (toInvSubmonoid_surjective M S)
108- rw [Monoid.fg_iff_submonoid_fg] at this
108+ rw [Monoid.fg_iff_submonoid_fg, Submonoid.fg_def ] at this
109109 rcases this with ⟨s, hs⟩
110110 refine ⟨⟨s, ?_⟩⟩
111111 rw [eq_top_iff]
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