mathlib documentation

data.int.char_zero

Injectivity of int.cast into characteristic zero rings and fields. #

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@[simp]
theorem int.cast_eq_zero {α : Type u_1} [add_group_with_one α] [char_zero α] {n : ℤ} :
↑n = 0 ↔ n = 0
source
@[simp, norm_cast]
theorem int.cast_inj {α : Type u_1} [add_group_with_one α] [char_zero α] {m n : ℤ} :
↑m = ↑n ↔ m = n
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theorem int.cast_injective {α : Type u_1} [add_group_with_one α] [char_zero α] :
function.injective coe
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theorem int.cast_ne_zero {α : Type u_1} [add_group_with_one α] [char_zero α] {n : ℤ} :
↑n ≠ 0 ↔ n ≠ 0
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@[simp, norm_cast]
theorem int.cast_div_char_zero {k : Type u_1} [division_ring k] [char_zero k] {m n : ℤ} (n_dvd : n ∣ m) :
↑(m / n) = ↑m / ↑n
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theorem ring_hom.injective_int {α : Type u_1} [non_assoc_ring α] (f : ℤ →+* α) [char_zero α] :
function.injective ⇑f