File: Mathlib/Data/Finsupp/Interval.lean

full_name: Finsupp.rangeSingleton_support
code: /-- Pointwise `Singleton.singleton` bundled as a `Finsupp`. -/
@[simps]
def rangeSingleton (f : ι →₀ α) : ι →₀ Finset α 
goal: f.rangeSingleton.support = f.support

full_name: Finsupp.rangeSingleton_toFun
code: /-- Pointwise `Singleton.singleton` bundled as a `Finsupp`. -/
@[simps]
def rangeSingleton (f : ι →₀ α) : ι →₀ Finset α 
goal: f.rangeSingleton i = {f i}

full_name: Finsupp.rangeSingleton
code: /-- Pointwise `Singleton.singleton` bundled as a `Finsupp`. -/
@[simps]
def rangeSingleton (f : ι →₀ α) : ι →₀ Finset α 
goal: ι →₀ Finset α

full_name: Finsupp.mem_rangeSingleton_apply_iff
code: theorem mem_rangeSingleton_apply_iff : a ∈ f.rangeSingleton i ↔ a = f i 
goal: a ∈ f.rangeSingleton i ↔ a = f i

full_name: Finsupp.rangeIcc_toFun
code: /-- Pointwise `Finset.Icc` bundled as a `Finsupp`. -/
@[simps toFun]
def rangeIcc (f g : ι →₀ α) : ι →₀ Finset α 
goal: (f.rangeIcc g) i = Finset.Icc (f i) (g i)

full_name: Finsupp.rangeIcc
code: /-- Pointwise `Finset.Icc` bundled as a `Finsupp`. -/
@[simps toFun]
def rangeIcc (f g : ι →₀ α) : ι →₀ Finset α 
goal: ι →₀ Finset α

full_name: Finsupp.coe_rangeIcc
code: lemma coe_rangeIcc (f g : ι →₀ α) : rangeIcc f g i = Icc (f i) (g i) 
goal: (f.rangeIcc g) i = Finset.Icc (f i) (g i)

full_name: Finsupp.rangeIcc_support
code: @[simp]
theorem rangeIcc_support (f g : ι →₀ α) :
    (rangeIcc f g).support = f.support ∪ g.support 
goal: (f.rangeIcc g).support = f.support ∪ g.support

full_name: Finsupp.mem_rangeIcc_apply_iff
code: theorem mem_rangeIcc_apply_iff : a ∈ f.rangeIcc g i ↔ f i ≤ a ∧ a ≤ g i 
goal: a ∈ (f.rangeIcc g) i ↔ f i ≤ a ∧ a ≤ g i

full_name: Finsupp.instLocallyFiniteOrder
code: instance instLocallyFiniteOrder : LocallyFiniteOrder (ι →₀ α) 
goal: LocallyFiniteOrder (ι →₀ α)

full_name: Finsupp.Icc_eq
code: theorem Icc_eq : Icc f g = (f.support ∪ g.support).finsupp (f.rangeIcc g) 
goal: Finset.Icc f g = (f.support ∪ g.support).finsupp ⇑(f.rangeIcc g)

full_name: Finsupp.card_Icc
code: theorem card_Icc : (Icc f g).card = ∏ i ∈ f.support ∪ g.support, (Icc (f i) (g i)).card 
goal: (Finset.Icc f g).card = ∏ i ∈ f.support ∪ g.support, (Finset.Icc (f i) (g i)).card

full_name: Finsupp.card_Ico
code: theorem card_Ico : (Ico f g).card = (∏ i ∈ f.support ∪ g.support, (Icc (f i) (g i)).card) - 1 
goal: (Finset.Ico f g).card = ∏ i ∈ f.support ∪ g.support, (Finset.Icc (f i) (g i)).card - 1

full_name: Finsupp.card_Ioc
code: theorem card_Ioc : (Ioc f g).card = (∏ i ∈ f.support ∪ g.support, (Icc (f i) (g i)).card) - 1 
goal: (Finset.Ioc f g).card = ∏ i ∈ f.support ∪ g.support, (Finset.Icc (f i) (g i)).card - 1

full_name: Finsupp.card_Ioo
code: theorem card_Ioo : (Ioo f g).card = (∏ i ∈ f.support ∪ g.support, (Icc (f i) (g i)).card) - 2 
goal: (Finset.Ioo f g).card = ∏ i ∈ f.support ∪ g.support, (Finset.Icc (f i) (g i)).card - 2

full_name: Finsupp.card_uIcc
code: theorem card_uIcc :
    (uIcc f g).card = ∏ i ∈ f.support ∪ g.support, (uIcc (f i) (g i)).card 
goal: (Finset.uIcc f g).card = ∏ i ∈ f.support ∪ g.support, (Finset.uIcc (f i) (g i)).card

full_name: Finsupp.card_Iic
code: theorem card_Iic : (Iic f).card = ∏ i ∈ f.support, (Iic (f i)).card 
goal: (Finset.Iic f).card = ∏ i ∈ f.support, (Finset.Iic (f i)).card

full_name: Finsupp.card_Iio
code: theorem card_Iio : (Iio f).card = (∏ i ∈ f.support, (Iic (f i)).card) - 1 
goal: (Finset.Iio f).card = ∏ i ∈ f.support, (Finset.Iic (f i)).card - 1