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[Merged by Bors] - lint(data/equiv/ring): docstrings, inhabited #4460

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[Merged by Bors] - lint(data/equiv/ring): docstrings, inhabited #4460

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17 changes: 16 additions & 1 deletion src/data/equiv/ring.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -37,12 +37,21 @@ variables {R : Type*} {S : Type*} {S' : Type*}

set_option old_structure_cmd true

/- (semi)ring equivalence. -/
/-- An equivalence between two (semi)rings that preserves the algebraic structure. -/
structure ring_equiv (R S : Type*) [has_mul R] [has_add R] [has_mul S] [has_add S]
extends R ≃ S, R ≃* S, R ≃+ S

infix ` ≃+* `:25 := ring_equiv

/-- The "plain" equivalence of types underlying an equivalence of (semi)rings. -/
add_decl_doc ring_equiv.to_equiv

/-- The equivalence of additive monoids underlying an equivalence of (semi)rings. -/
add_decl_doc ring_equiv.to_add_equiv

/-- The equivalence of multiplicative monoids underlying an equivalence of (semi)rings. -/
add_decl_doc ring_equiv.to_mul_equiv

namespace ring_equiv

section basic
Expand Down Expand Up @@ -84,6 +93,8 @@ variable (R)

@[simp] lemma coe_mul_equiv_refl : (ring_equiv.refl R : R ≃* R) = mul_equiv.refl R := rfl

instance : inhabited (R ≃+* R) := ⟨ring_equiv.refl R⟩

variables {R}

/-- The inverse of a ring isomorphism is a ring isomorphism. -/
Expand Down Expand Up @@ -313,6 +324,10 @@ namespace equiv

variables (K : Type*) [division_ring K]

/-- In a division ring `K`, the unit group `units K`
is equivalent to the subtype of nonzero elements. -/
-- TODO: this might already exist elsewhere for `group_with_zero`
-- deduplicate or generalize
def units_equiv_ne_zero : units K ≃ {a : K | a ≠ 0} :=
⟨λ a, ⟨a.1, a.ne_zero⟩, λ a, units.mk0 _ a.2, λ ⟨_, _, _, _⟩, units.ext rfl, λ ⟨_, _⟩, rfl⟩

Expand Down