Typeclass expressing 0 ≤ 1.

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

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.

@[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.

instance ZeroLEOneClass.factZeroLeOne {α : Type u_1} [Zero α] [One α] [LE α] [ZeroLEOneClass α] : Fact (0 ≤ 1)

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.

instance Prod.instZeroLEOneClass {R : Type u_2} {S : Type u_3} [Zero R] [One R] [LE R] [ZeroLEOneClass R] [Zero S] [One S] [LE S] [ZeroLEOneClass S] : ZeroLEOneClass (R × S)

instance Pi.instZeroLEOneClass {ι : Type u_2} {R : ι → Type u_3} [(i : ι) → Zero (R i)] [(i : ι) → One (R i)] [(i : ι) → LE (R i)] [∀ (i : ι), ZeroLEOneClass (R i)] : ZeroLEOneClass ((i : ι) → R i)

@[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.

instance ZeroLEOneClass.factZeroLtOne {α : Type u_1} [Zero α] [One α] [PartialOrder α] [ZeroLEOneClass α] [NeZero 1] : Fact (0 < 1)

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.

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See zero_lt_one' for a version with the type explicit.