Lemire.div_one: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend as Lemire
Lines 461-463 of bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&start_line=461&end_line=463

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend as AR
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

def div_one(+N: Nat) -> {Nat.div(N, 1n) == N : Nat}:
  %Equal.sym(Nat, N, Nat.add(Nat.mul(N, 1n), 0n), Equal.trans(Nat, N, Nat.mul(N, 1n), Nat.add(Nat.mul(N, 1n), 0n), Equal.sym(Nat, Nat.mul(N, 1n), N, NA.mul_one(N)), Equal.sym(Nat, Nat.add(Nat.mul(N, 1n), 0n), Nat.mul(N, 1n), N.add_zero(Nat.mul(N, 1n))))) : {Nat.div(_, 1n) == N : Nat}
  AR.div_of(N, 0n, 0n, {==})

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=mul_one
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&name=div_of