Arith.mod_mod: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend as Arith
Lines 131-133 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&start_line=131&end_line=133

import Base

# (x mod n) mod n == x mod n   (Mathlib Nat.mod_mod)
def mod_mod(+bp: Nat, +x: Nat) -> {Nat.mod(Nat.mod(x, 1n+bp), 1n+bp) == Nat.mod(x, 1n+bp) : Nat}:
  mod_of(0n, bp, Nat.mod(x, 1n+bp), dm_lt(bp, x))

Uses (4):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&name=dm_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&name=mod_of