Natural.ModInverse.not_coprime: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/spec/math/natural.bend as Natural
Lines 265-267 of bend-collections-laws-math@1.0.0.0/spec/math/natural.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/natural.bend&start_line=265&end_line=267

import Base
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M

# PDF 8.7: no inverse exactly when a and m share a factor g >= 2
def ModInverse.not_coprime(+a: Nat, +mp: Nat, +h: {M.mod_inverse(a, 1n+mp) == Fail{M.NotInvertible{}} : Result<&2, &2, M.MathError, Nat>}) -> Type:
  Sigma<&1, &1, Nat, g => {Nat.is_le(2n, g) == True{} : Bool} & (dvd(g, a) & dvd(g, 1n+mp))>

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/natural.bend&name=dvd
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=MathError
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/natural.bend&name=mod_inverse