def pm_pick

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64int.bend:482

import Base
import bend-collections-laws-math@1.0.0.0/src/math/generic.bend as G
import bend-collections-laws-math@1.0.0.0/src/math/natural.bend as M
import bend-collections-laws-math@1.0.0.0/src/math/instances.bend as I
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X

482def pm_pick(+k: Nat, +hk: {k == 64n : Nat}, +b: WU.U64, +e: WU.U64, +m: WU.U64, +mp: Nat, +hnm: {v(m) == 1n+mp : Nat}, +c: Bool, +hc: {X.mont_ok(m) == c : Bool}) -> {v(G.pow_mod_pick(~WU.U64, ~I.u64_op, ~I.u64_is, b, e, m, c)) == M.pow_mod_go(v(e), 1n+mp, v(e), Nat.mod(v(b), 1n+mp), Nat.mod(1n, 1n+mp)) : Nat}:
483  match c:
484    case True{}:
485      pm_mont(k, hk, b, e, m, mp, hnm, hc)
486    case False{}:
487      pm_gen(k, hk, b, e, m, mp, hnm)