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core.​init.​data.​fin.​ops

core.​init.​data.​fin.​ops

source
fin.​add
fin.​add_def
fin.​div
fin.​div_def
fin.​has_add
fin.​has_div
fin.​has_mod
fin.​has_mul
fin.​has_one
fin.​has_sub
fin.​has_zero
fin.​le_def
fin.​lt_def
fin.​mod
fin.​mod_def
fin.​mul
fin.​mul_def
fin.​of_nat
fin.​of_nat_zero
fin.​pred
fin.​sub
fin.​sub_def
fin.​succ
fin.​val_zero
source
def fin.​succ {n : ℕ} :
fin n → fin n.succ

Equations
source
def fin.​of_nat {n : ℕ} :
ℕ → fin n.succ

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source
def fin.​add {n : ℕ} :
fin n → fin n → fin n

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source
def fin.​mul {n : ℕ} :
fin n → fin n → fin n

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source
def fin.​sub {n : ℕ} :
fin n → fin n → fin n

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source
def fin.​mod {n : ℕ} :
fin n → fin n → fin n

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source
def fin.​div {n : ℕ} :
fin n → fin n → fin n

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source
@[instance]
def fin.​has_zero {n : ℕ} :
has_zero (fin n.succ)

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source
@[instance]
def fin.​has_one {n : ℕ} :
has_one (fin n.succ)

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source
@[instance]
def fin.​has_add {n : ℕ} :
has_add (fin n)

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source
@[instance]
def fin.​has_sub {n : ℕ} :
has_sub (fin n)

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source
@[instance]
def fin.​has_mul {n : ℕ} :
has_mul (fin n)

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source
@[instance]
def fin.​has_mod {n : ℕ} :
has_mod (fin n)

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source
@[instance]
def fin.​has_div {n : ℕ} :
has_div (fin n)

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source
theorem fin.​of_nat_zero {n : ℕ} :
fin.of_nat 0 = 0

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theorem fin.​add_def {n : ℕ} (a b : fin n) :
(a + b).val = (a.val + b.val) % n

source
theorem fin.​mul_def {n : ℕ} (a b : fin n) :
(a * b).val = a.val * b.val % n

source
theorem fin.​sub_def {n : ℕ} (a b : fin n) :
(a - b).val = a.val - b.val

source
theorem fin.​mod_def {n : ℕ} (a b : fin n) :
(a % b).val = a.val % b.val

source
theorem fin.​div_def {n : ℕ} (a b : fin n) :
(a / b).val = a.val / b.val

source
theorem fin.​lt_def {n : ℕ} (a b : fin n) :
a < b = (a.val < b.val)

source
theorem fin.​le_def {n : ℕ} (a b : fin n) :
a ≤ b = (a.val ≤ b.val)

source
@[simp]
theorem fin.​val_zero {n : ℕ} :
0.val = 0

source
def fin.​pred {n : ℕ} (i : fin n.succ) :
i ≠ 0 → fin n

Equations

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