def inverse_done

bend-collections-laws-crypto@1.0.0.0 · proofs/math/natural/inverse.bend:185

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

185# mod_inverse(a, m) == Done{x}: a x == 1 (mod m) and x < m   (Mathlib ZMod.mul_inv_of_unit)
186def inverse_done(+a: Nat, +mp: Nat, +x: Nat, +h: {M.mod_inverse(a, 1n+mp) == Done{x} : Result<&2, &2, M.MathError, Nat>}) -> {Nat.mod(Nat.mul(a, x), 1n+mp) == Nat.mod(1n, 1n+mp) : Nat} & {Nat.is_lt(x, 1n+mp) == True{} : Bool}:
187  done_bz(mp, a, inv_bz(a, mp), inv_bezout(a, mp), x, h)