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fix(data/equiv): nolint typo (#4677)
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Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com>
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fpvandoorn and bryangingechen committed Oct 19, 2020
1 parent 49bb5dd commit 9d1bbd1
Showing 1 changed file with 9 additions and 5 deletions.
14 changes: 9 additions & 5 deletions src/data/equiv/basic.lean
Expand Up @@ -48,7 +48,8 @@ Then we define
More definitions of this kind can be found in other files. E.g., `data/equiv/transfer_instance`
does it for many algebraic type classes like `group`, `module`, etc.
* group structure on `equiv.perm α`. More lemmas about `equiv.perm` can be found in `data/equiv/perm`.
* group structure on `equiv.perm α`. More lemmas about `equiv.perm` can be found in
`data/equiv/perm`.
## Tags
Expand All @@ -61,7 +62,7 @@ universes u v w z
variables {α : Sort u} {β : Sort v} {γ : Sort w}

/-- `α ≃ β` is the type of functions from `α → β` with a two-sided inverse. -/
@[nolint inhabited]
@[nolint has_inhabited_instance]
structure equiv (α : Sort*) (β : Sort*) :=
(to_fun : α → β)
(inv_fun : β → α)
Expand Down Expand Up @@ -788,7 +789,8 @@ def sigma_congr_left {α₁ α₂} {β : α₂ → Sort*} (e : α₁ ≃ α₂)
λ ⟨a, b⟩, match e.symm (e a), e.left_inv a : ∀ a' (h : a' = a),
@sigma.mk _ (β ∘ e) _ (@@eq.rec β b (congr_arg e h.symm)) = ⟨a, b⟩ with
| _, rfl := rfl end,
λ ⟨a, b⟩, match e (e.symm a), _ : ∀ a' (h : a' = a), sigma.mk a' (@@eq.rec β b h.symm) = ⟨a, b⟩ with
λ ⟨a, b⟩, match e (e.symm a), _ : ∀ a' (h : a' = a),
sigma.mk a' (@@eq.rec β b h.symm) = ⟨a, b⟩ with
| _, rfl := rfl end

@[simp] lemma sigma_congr_left_apply {α₁ α₂} {β : α₂ → Sort*} (e : α₁ ≃ α₂) (x : Σ a, β (e a)) :
Expand Down Expand Up @@ -1351,7 +1353,8 @@ by cases x with x hx; exact set.sum_compl_symm_apply_of_not_mem hx
`s ⊕ (t \ s)` and `t`, where `s` and `t` are two sets. -/
protected def sum_diff_subset {α} {s t : set α} (h : s ⊆ t) [decidable_pred s] :
s ⊕ (t \ s : set α) ≃ t :=
calc s ⊕ (t \ s : set α) ≃ (s ∪ (t \ s) : set α) : (equiv.set.union (by simp [inter_diff_self])).symm
calc s ⊕ (t \ s : set α) ≃ (s ∪ (t \ s) : set α) :
(equiv.set.union (by simp [inter_diff_self])).symm
... ≃ t : equiv.set.of_eq (by { simp [union_diff_self, union_eq_self_of_subset_left h] })

@[simp] lemma sum_diff_subset_apply_inl
Expand Down Expand Up @@ -1494,7 +1497,8 @@ noncomputable def of_bijective {α β} (f : α → β) (hf : bijective f) : α

/-- If `f` is an injective function, then its domain is equivalent to its range. -/
noncomputable def of_injective {α β} (f : α → β) (hf : injective f) : α ≃ _root_.set.range f :=
of_bijective (λ x, ⟨f x, set.mem_range_self x⟩) ⟨λ x y hxy, hf $ by injections, λ ⟨_, x, rfl⟩, ⟨x, rfl⟩⟩
of_bijective (λ x, ⟨f x, set.mem_range_self x⟩)
⟨λ x y hxy, hf $ by injections, λ ⟨_, x, rfl⟩, ⟨x, rfl⟩⟩

@[simp] lemma of_injective_apply {α β} (f : α → β) (hf : injective f) (x : α) :
of_injective f hf x = ⟨f x, set.mem_range_self x⟩ :=
Expand Down

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