def reduced

bend-collections-laws-math@1.0.0.0 · proofs/math/natural/proof.bend:171

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

171def reduced(+a: Nat, +mp: Nat, +x: Nat, +h: {M.mod_inverse(a, 1n+mp) == Done{x} : Result<&2, &2, M.MathError, Nat>}) -> S.ModInverse.reduced(a, mp, x, h):
172  Pair.snd({Nat.mod(Nat.mul(a, x), 1n+mp) == Nat.mod(1n, 1n+mp) : Nat}, {Nat.is_lt(x, 1n+mp) == True{} : Bool}, IV.inverse_done(a, mp, x, h))