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data.​fintype.​intervals

data.​fintype.​intervals

source
set.​Ico_pnat_card
set.​Ico_pnat_fintype
set.​Ico_ℕ_card
set.​Ico_ℕ_fintype
set.​Ico_ℤ_card
set.​Ico_ℤ_fintype

fintype instances for intervals

We provide fintype instances for Ico l u, for l u : ℕ, and for l u : ℤ.

source
@[instance]
def set.​Ico_ℕ_fintype (l u : ℕ) :
fintype ↥(set.Ico l u)

Equations
source
@[simp]
theorem set.​Ico_ℕ_card (l u : ℕ) :
fintype.card ↥(set.Ico l u) = u - l

source
@[instance]
def set.​Ico_pnat_fintype (l u : ℕ+) :
fintype ↥(set.Ico l u)

Equations
source
@[simp]
theorem set.​Ico_pnat_card (l u : ℕ+) :
fintype.card ↥(set.Ico l u) = ↑u - ↑l

source
@[instance]
def set.​Ico_ℤ_fintype (l u : ℤ) :
fintype ↥(set.Ico l u)

Equations
source
@[simp]
theorem set.​Ico_ℤ_card (l u : ℤ) :
fintype.card ↥(set.Ico l u) = (u - l).to_nat

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