Lemire.bitsq_b: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/random/lemire.bend as Lemire
Lines 474-482 of bend-collections-laws-crypto@1.0.0.0/proofs/math/random/lemire.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/random/lemire.bend&start_line=474&end_line=482

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L

# bit * bit == bit
def bitsq_b(+b: Nat, +h: {Nat.is_le(b, 1n) == True{} : Bool}) -> {Nat.mul(b, b) == b : Nat}:
  match b:
    case 0n:
      {==}
    case 1n:
      {==}
    case 2n+q:
      Empty.absurd({Nat.mul(2n+q, 2n+q) == 2n+q : Nat}, L.false_true(h))

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=false_true