Documentation

Mathlib.Algebra.Order.ZeroLEOne

Typeclass expressing 0 ≤ 1. #

class ZeroLEOneClass (α : Type u_2) [Zero α] [One α] [LE α] :

Typeclass for expressing that the 0 of a type is less or equal to its 1.

  • zero_le_one : 0 1

    Zero is less than or equal to one.

Instances
    @[simp]
    theorem zero_le_one {α : Type u_1} [Zero α] [One α] [LE α] [ZeroLEOneClass α] :
    0 1

    zero_le_one with the type argument implicit.

    theorem zero_le_one' (α : Type u_2) [Zero α] [One α] [LE α] [ZeroLEOneClass α] :
    0 1

    zero_le_one with the type argument explicit.

    @[simp]
    theorem zero_lt_one {α : Type u_1} [Zero α] [One α] [PartialOrder α] [ZeroLEOneClass α] [NeZero 1] :
    0 < 1

    See zero_lt_one' for a version with the type explicit.

    theorem zero_lt_one' (α : Type u_1) [Zero α] [One α] [PartialOrder α] [ZeroLEOneClass α] [NeZero 1] :
    0 < 1

    See zero_lt_one for a version with the type implicit.

    theorem one_pos {α : Type u_1} [Zero α] [One α] [PartialOrder α] [ZeroLEOneClass α] [NeZero 1] :
    0 < 1

    Alias of zero_lt_one.


    See zero_lt_one' for a version with the type explicit.