File: Mathlib/Algebra/Order/Ring/InjSurj.lean

full_name: Function.Injective.orderedSemiring
code: /-- Pullback an `OrderedSemiring` under an injective map. -/
-- See note [reducible non-instances]
protected abbrev orderedSemiring [OrderedSemiring α] (zero : f 0 = 0) (one : f 1 = 1)
    (add : ∀ x y, f (x + y) = f x + f y) (mul : ∀ x y, f (x * y) = f x * f y)
    (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x) (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n)
    (natCast : ∀ n : ℕ, f n = n) : OrderedSemiring β 
goal: OrderedSemiring β

full_name: Function.Injective.orderedCommSemiring
code: /-- Pullback an `OrderedCommSemiring` under an injective map. -/
-- See note [reducible non-instances]
protected abbrev orderedCommSemiring [OrderedCommSemiring α] (zero : f 0 = 0) (one : f 1 = 1)
    (add : ∀ x y, f (x + y) = f x + f y) (mul : ∀ x y, f (x * y) = f x * f y)
    (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x) (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n)
    (natCast : ∀ n : ℕ, f n = n) : OrderedCommSemiring β 
goal: OrderedCommSemiring β

full_name: Function.Injective.orderedRing
code: /-- Pullback an `OrderedRing` under an injective map. -/
-- See note [reducible non-instances]
protected abbrev orderedRing [OrderedRing α] (zero : f 0 = 0) (one : f 1 = 1)
    (add : ∀ x y, f (x + y) = f x + f y)
    (mul : ∀ x y, f (x * y) = f x * f y) (neg : ∀ x, f (-x) = -f x)
    (sub : ∀ x y, f (x - y) = f x - f y) (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x)
    (zsmul : ∀ (n : ℤ) (x), f (n • x) = n • f x) (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n)
    (natCast : ∀ n : ℕ, f n = n) (intCast : ∀ n : ℤ, f n = n) : OrderedRing β 
goal: OrderedRing β

full_name: Function.Injective.orderedCommRing
code: /-- Pullback an `OrderedCommRing` under an injective map. -/
-- See note [reducible non-instances]
protected abbrev orderedCommRing [OrderedCommRing α]
    (zero : f 0 = 0) (one : f 1 = 1) (add : ∀ x y, f (x + y) = f x + f y)
    (mul : ∀ x y, f (x * y) = f x * f y) (neg : ∀ x, f (-x) = -f x)
    (sub : ∀ x y, f (x - y) = f x - f y) (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x)
    (zsmul : ∀ (n : ℤ) (x), f (n • x) = n • f x) (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n)
    (natCast : ∀ n : ℕ, f n = n) (intCast : ∀ n : ℤ, f n = n) : OrderedCommRing β 
goal: OrderedCommRing β

full_name: Function.Injective.strictOrderedSemiring
code: /-- Pullback a `StrictOrderedSemiring` under an injective map. -/
-- See note [reducible non-instances]
protected abbrev strictOrderedSemiring [StrictOrderedSemiring α] (zero : f 0 = 0) (one : f 1 = 1)
    (add : ∀ x y, f (x + y) = f x + f y) (mul : ∀ x y, f (x * y) = f x * f y)
    (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x) (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n)
    (natCast : ∀ n : ℕ, f n = n) : StrictOrderedSemiring β 
goal: StrictOrderedSemiring β

full_name: Function.Injective.strictOrderedCommSemiring
code: /-- Pullback a `strictOrderedCommSemiring` under an injective map. -/
-- See note [reducible non-instances]
protected abbrev strictOrderedCommSemiring [StrictOrderedCommSemiring α]
    (zero : f 0 = 0) (one : f 1 = 1)
    (add : ∀ x y, f (x + y) = f x + f y) (mul : ∀ x y, f (x * y) = f x * f y)
    (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x) (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n)
    (natCast : ∀ n : ℕ, f n = n) : StrictOrderedCommSemiring β 
goal: StrictOrderedCommSemiring β

full_name: Function.Injective.strictOrderedRing
code: /-- Pullback a `StrictOrderedRing` under an injective map. -/
-- See note [reducible non-instances]
protected abbrev strictOrderedRing [StrictOrderedRing α] (zero : f 0 = 0) (one : f 1 = 1)
    (add : ∀ x y, f (x + y) = f x + f y) (mul : ∀ x y, f (x * y) = f x * f y)
    (neg : ∀ x, f (-x) = -f x) (sub : ∀ x y, f (x - y) = f x - f y)
    (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x) (zsmul : ∀ (n : ℤ) (x), f (n • x) = n • f x)
    (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n)
    (natCast : ∀ n : ℕ, f n = n) (intCast : ∀ n : ℤ, f n = n) : StrictOrderedRing β 
goal: StrictOrderedRing β

full_name: Function.Injective.strictOrderedCommRing
code: /-- Pullback a `StrictOrderedCommRing` under an injective map. -/
-- See note [reducible non-instances]
protected abbrev strictOrderedCommRing [StrictOrderedCommRing α] (zero : f 0 = 0) (one : f 1 = 1)
    (add : ∀ x y, f (x + y) = f x + f y)
    (mul : ∀ x y, f (x * y) = f x * f y) (neg : ∀ x, f (-x) = -f x)
    (sub : ∀ x y, f (x - y) = f x - f y) (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x)
    (zsmul : ∀ (n : ℤ) (x), f (n • x) = n • f x) (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n)
    (natCast : ∀ n : ℕ, f n = n) (intCast : ∀ n : ℤ, f n = n) : StrictOrderedCommRing β 
goal: StrictOrderedCommRing β

full_name: Function.Injective.linearOrderedSemiring
code: /-- Pullback a `LinearOrderedSemiring` under an injective map. -/
-- See note [reducible non-instances]
protected abbrev linearOrderedSemiring [LinearOrderedSemiring α] (zero : f 0 = 0) (one : f 1 = 1)
    (add : ∀ x y, f (x + y) = f x + f y) (mul : ∀ x y, f (x * y) = f x * f y)
    (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x)
    (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n) (natCast : ∀ n : ℕ, f n = n)
    (sup : ∀ x y, f (x ⊔ y) = max (f x) (f y)) (inf : ∀ x y, f (x ⊓ y) = min (f x) (f y)) :
    LinearOrderedSemiring β 
goal: LinearOrderedSemiring β

full_name: Function.Injective.linearOrderedCommSemiring
code: /-- Pullback a `LinearOrderedSemiring` under an injective map. -/
-- -- See note [reducible non-instances]
protected abbrev linearOrderedCommSemiring [LinearOrderedCommSemiring α]
    (zero : f 0 = 0) (one : f 1 = 1) (add : ∀ x y, f (x + y) = f x + f y)
    (mul : ∀ x y, f (x * y) = f x * f y) (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x)
    (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n) (natCast : ∀ n : ℕ, f n = n)
    (hsup : ∀ x y, f (x ⊔ y) = max (f x) (f y)) (hinf : ∀ x y, f (x ⊓ y) = min (f x) (f y)) :
    LinearOrderedCommSemiring β 
goal: LinearOrderedCommSemiring β

full_name: Function.Injective.linearOrderedRing
code: /-- Pullback a `LinearOrderedRing` under an injective map. -/
-- See note [reducible non-instances]
abbrev linearOrderedRing [LinearOrderedRing α] (zero : f 0 = 0) (one : f 1 = 1)
    (add : ∀ x y, f (x + y) = f x + f y) (mul : ∀ x y, f (x * y) = f x * f y)
    (neg : ∀ x, f (-x) = -f x) (sub : ∀ x y, f (x - y) = f x - f y)
    (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x) (zsmul : ∀ (n : ℤ) (x), f (n • x) = n • f x)
    (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n)
    (natCast : ∀ n : ℕ, f n = n) (intCast : ∀ n : ℤ, f n = n)
    (hsup : ∀ x y, f (x ⊔ y) = max (f x) (f y)) (hinf : ∀ x y, f (x ⊓ y) = min (f x) (f y)) :
    LinearOrderedRing β 
goal: LinearOrderedRing β

full_name: Function.Injective.linearOrderedCommRing
code: /-- Pullback a `LinearOrderedCommRing` under an injective map. -/
-- See note [reducible non-instances]
protected abbrev linearOrderedCommRing [LinearOrderedCommRing α] (zero : f 0 = 0) (one : f 1 = 1)
    (add : ∀ x y, f (x + y) = f x + f y) (mul : ∀ x y, f (x * y) = f x * f y)
    (neg : ∀ x, f (-x) = -f x) (sub : ∀ x y, f (x - y) = f x - f y)
    (nsmul : ∀ (n : ℕ) (x), f (n • x) = n • f x) (zsmul : ∀ (n : ℤ) (x), f (n • x) = n • f x)
    (npow : ∀ (x) (n : ℕ), f (x ^ n) = f x ^ n) (natCast : ∀ n : ℕ, f n = n)
    (intCast : ∀ n : ℤ, f n = n) (sup : ∀ x y, f (x ⊔ y) = max (f x) (f y))
    (inf : ∀ x y, f (x ⊓ y) = min (f x) (f y)) : LinearOrderedCommRing β 
goal: LinearOrderedCommRing β