mirror of
https://github.com/Smaug123/agdaproofs
synced 2025-10-13 07:38:40 +00:00
28 lines
860 B
Agda
28 lines
860 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
|
||
|
||
open import LogicalFormulae
|
||
open import Groups.Definition
|
||
open import Groups.Groups
|
||
open import Groups.Abelian.Definition
|
||
open import Groups.FiniteGroups.Definition
|
||
open import Numbers.Naturals.Semiring
|
||
open import Numbers.Naturals.Naturals
|
||
open import Numbers.Naturals.Order
|
||
open import Setoids.Setoids
|
||
open import Sets.FinSet.Definition
|
||
open import Functions
|
||
open import Semirings.Definition
|
||
open import Numbers.Naturals.EuclideanAlgorithm
|
||
open import Orders.Total.Definition
|
||
|
||
module Numbers.Modulo.Definition where
|
||
|
||
record ℤn (n : ℕ) .(pr : 0 <N n) : Set where
|
||
field
|
||
x : ℕ
|
||
.xLess : x <N n
|
||
|
||
equalityZn : {n : ℕ} .{pr : 0 <N n} → {a b : ℤn n pr} → (ℤn.x a ≡ ℤn.x b) → a ≡ b
|
||
equalityZn {a = record { x = a ; xLess = aLess }} {record { x = .a ; xLess = bLess }} refl = refl
|
||
|