@@ -127,8 +127,8 @@ def symmetricSubgroup (A : Finset G) (h : #(A * A) < (3 / 2 : ℚ) * #A) : Subgr
127127 rw [← coe_mul_comm_of_doubling (weaken_doubling h)]
128128 exact ⟨a * b * t, by simp [ht, mul_assoc], ((c * d)⁻¹ * t)⁻¹, by simp [ht, mul_assoc]⟩
129129
130- lemma coe_symmetricSubgroup (A : Finset G) (h) : (symmetricSubgroup A h : Set G) = A * A⁻¹ := by
131- rw [symmetricSubgroup_coe , eq_comm]
130+ lemma coe_symmetricSubgroup' (A : Finset G) (h) : (symmetricSubgroup A h : Set G) = A * A⁻¹ := by
131+ rw [coe_symmetricSubgroup , eq_comm]
132132 norm_cast
133133 exact mul_comm_of_doubling (by qify at h ⊢; linarith)
134134
@@ -180,7 +180,7 @@ lemma A_subset_aH (a : G) (ha : a ∈ A) : A ⊆ a • (A⁻¹ * A) := by
180180lemma subgroup_strong_bound_left (h : #(A * A) < (3 / 2 : ℚ) * #A) (a : G) (ha : a ∈ A) :
181181 A * A ⊆ a • op a • (A⁻¹ * A) := by
182182 have h₁ : (A⁻¹ * A) * (A⁻¹ * A) = A⁻¹ * A := by
183- rw [← coe_inj, coe_mul, coe_mul, ← symmetricSubgroup_coe _ h, coe_mul_coe]
183+ rw [← coe_inj, coe_mul, coe_mul, ← coe_symmetricSubgroup _ h, coe_mul_coe]
184184 have h₂ : a • op a • (A⁻¹ * A) = (a • (A⁻¹ * A)) * (op a • (A⁻¹ * A)) := by
185185 rw [mul_smul_comm, smul_mul_assoc, h₁, smul_comm]
186186 rw [h₂]
@@ -246,19 +246,19 @@ theorem very_small_doubling (h : #(A * A) < (3 / 2 : ℚ) * #A) :
246246 refine ⟨H, inferInstance, ?_, fun a ha ↦ ⟨?_, subset_antisymm ?_ ?_⟩⟩
247247 · simp [← Nat.card_eq_fintype_card, symmetricSubgroup, ← coe_mul, ← coe_inv, H]
248248 rwa [Nat.card_eq_finsetCard, subgroup_strong_bound h]
249- · rw [symmetricSubgroup_coe ]
249+ · rw [coe_symmetricSubgroup ]
250250 exact_mod_cast A_subset_aH a ha
251251 · rw [Set.subset_set_smul_iff, ← op_inv]
252252 calc
253253 a •> (H : Set G) <• a⁻¹ ⊆ a •> (H : Set G) * A⁻¹ := Set.op_smul_set_subset_mul (by simpa)
254254 _ ⊆ A * (H : Set G) * A⁻¹ := by gcongr; exact Set.smul_set_subset_mul (by simpa)
255255 _ = H := by
256- rw [symmetricSubgroup_coe , ← mul_assoc, ← coe_symmetricSubgroup _ h, mul_assoc,
257- ← coe_symmetricSubgroup _ h, ← symmetricSubgroup_coe _ h, coe_mul_coe]
256+ rw [coe_symmetricSubgroup , ← mul_assoc, ← coe_symmetricSubgroup' _ h, mul_assoc,
257+ ← coe_symmetricSubgroup' _ h, ← coe_symmetricSubgroup _ h, coe_mul_coe]
258258 · rw [Set.subset_set_smul_iff]
259259 calc
260260 a⁻¹ •> ((H : Set G) <• a) ⊆ A⁻¹ * (H : Set G) <• a := Set.smul_set_subset_mul (by simpa)
261261 _ ⊆ A⁻¹ * ((H : Set G) * A) := by gcongr; exact Set.op_smul_set_subset_mul (by simpa)
262262 _ = H := by
263- rw [coe_symmetricSubgroup, mul_assoc, ← symmetricSubgroup_coe _ h, ← mul_assoc,
264- ← symmetricSubgroup_coe _ h, ← coe_symmetricSubgroup _ h, coe_mul_coe]
263+ rw [coe_symmetricSubgroup' , mul_assoc, ← coe_symmetricSubgroup _ h, ← mul_assoc,
264+ ← coe_symmetricSubgroup _ h, ← coe_symmetricSubgroup' _ h, coe_mul_coe]
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