Pulling back linearly ordered fields along injective maps #

@[reducible, inline]
abbrev Function.Injective.linearOrderedSemifield {α : Type u_2} {β : Type u_3} [Zero β] [One β] [Add β] [Mul β] [Pow β ] [] [] [] [] [Inv β] [Div β] [Pow β ] [Sup β] [Inf β] (f : βα) (hf : ) (zero : f 0 = 0) (one : f 1 = 1) (add : ∀ (x y : β), f (x + y) = f x + f y) (mul : ∀ (x y : β), f (x * y) = f x * f y) (inv : ∀ (x : β), f x⁻¹ = (f x)⁻¹) (div : ∀ (x y : β), f (x / y) = f x / f y) (nsmul : ∀ (n : ) (x : β), f (n x) = n f x) (nnqsmul : ∀ (q : ℚ≥0) (x : β), f (q x) = q f x) (npow : ∀ (x : β) (n : ), f (x ^ n) = f x ^ n) (zpow : ∀ (x : β) (n : ), f (x ^ n) = f x ^ n) (natCast : ∀ (n : ), f n = n) (nnratCast : ∀ (q : ℚ≥0), f q = q) (hsup : ∀ (x y : β), f (x y) = max (f x) (f y)) (hinf : ∀ (x y : β), f (x y) = min (f x) (f y)) :

Pullback a LinearOrderedSemifield under an injective map.

Equations
• One or more equations did not get rendered due to their size.
Instances For
@[reducible, inline]
abbrev Function.Injective.linearOrderedField {α : Type u_2} {β : Type u_3} [Zero β] [One β] [Add β] [Mul β] [Neg β] [Sub β] [Pow β ] [] [] [] [] [] [] [] [] [Inv β] [Div β] [Pow β ] [Sup β] [Inf β] (f : βα) (hf : ) (zero : f 0 = 0) (one : f 1 = 1) (add : ∀ (x y : β), f (x + y) = f x + f y) (mul : ∀ (x y : β), f (x * y) = f x * f y) (neg : ∀ (x : β), f (-x) = -f x) (sub : ∀ (x y : β), f (x - y) = f x - f y) (inv : ∀ (x : β), f x⁻¹ = (f x)⁻¹) (div : ∀ (x y : β), f (x / y) = f x / f y) (nsmul : ∀ (n : ) (x : β), f (n x) = n f x) (zsmul : ∀ (n : ) (x : β), f (n x) = n f x) (nnqsmul : ∀ (q : ℚ≥0) (x : β), f (q x) = q f x) (qsmul : ∀ (q : ) (x : β), f (q x) = q f x) (npow : ∀ (x : β) (n : ), f (x ^ n) = f x ^ n) (zpow : ∀ (x : β) (n : ), f (x ^ n) = f x ^ n) (natCast : ∀ (n : ), f n = n) (intCast : ∀ (n : ), f n = n) (nnratCast : ∀ (q : ℚ≥0), f q = q) (ratCast : ∀ (q : ), f q = q) (hsup : ∀ (x y : β), f (x y) = max (f x) (f y)) (hinf : ∀ (x y : β), f (x y) = min (f x) (f y)) :

Pullback a LinearOrderedField under an injective map.

Equations
• One or more equations did not get rendered due to their size.
Instances For