Proof.not_coprime: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend as Proof
Lines 180-181 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend&start_line=180&end_line=181

import Base
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/spec/math/natural.bend as S
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend as IV

def not_coprime(+a: Nat, +mp: Nat, +h: {M.mod_inverse(a, 1n+mp) == Fail{M.NotInvertible{}} : Result<&2, &2, M.MathError, Nat>}) -> S.ModInverse.not_coprime(a, mp, h):
  (IV.bg(IV.inv_bz(a, mp)), factor_parts(a, mp, IV.bg(IV.inv_bz(a, mp)), IV.inv_ka(a, mp), IV.inv_km(a, mp), IV.inverse_fail(a, mp, h)))

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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/proofs/math/natural/inverse.bend&name=bg
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend&name=inv_bz
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend&name=inv_ka
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend&name=inv_km
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/inverse.bend&name=inverse_fail
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/proof.bend&name=factor_parts
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/natural.bend&name=ModInverse.not_coprime
  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