NatOrder.rhd.c2a.k: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/nat_order.bend as NatOrder
Lines 617-635 of bend-kit-collections@0.1.4.1/nat_order.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&start_line=617&end_line=635

import Base

def rhd.c2a.k(+l: Nat, +x: Nat, +y: Nat, +b: Nat, ng: LE(1n+Nat.mul(3n, x), l), h3: LE(1n+Nat.mul(3n, l), Nat.add(b, Nat.add(y, x))), hd: LE(Nat.mul(2n, b), Nat.add(y, x)), h6: LE(y, Nat.mul(3n, x))) -> Empty:
  +v = {VS{l, x, y, b} : Vs}
  +f_ng = cvle(1n+Nat.mul(3n, x), l, L{1n, 0n, 3n, 0n, 0n}, L{0n, 1n, 0n, 0n, 0n}, v,
    cv_add(1n, Nat.mul(3n, x), L{1n, 0n, 0n, 0n, 0n}, L{0n, 0n, 3n, 0n, 0n}, v, cv_c(1n, v), cv_mul(3n, x, L{0n, 0n, 1n, 0n, 0n}, v, cv_2(l, x, y, b))),
    cv_1(l, x, y, b), ng)
  +f_h3 = cvle(1n+Nat.mul(3n, l), Nat.add(b, Nat.add(y, x)), L{1n, 3n, 0n, 0n, 0n}, L{0n, 0n, 1n, 1n, 1n}, v,
    cv_add(1n, Nat.mul(3n, l), L{1n, 0n, 0n, 0n, 0n}, L{0n, 3n, 0n, 0n, 0n}, v, cv_c(1n, v), cv_mul(3n, l, L{0n, 1n, 0n, 0n, 0n}, v, cv_1(l, x, y, b))),
    cv_add(b, Nat.add(y, x), L{0n, 0n, 0n, 0n, 1n}, L{0n, 0n, 1n, 1n, 0n}, v, cv_4(l, x, y, b), cv_add(y, x, L{0n, 0n, 0n, 1n, 0n}, L{0n, 0n, 1n, 0n, 0n}, v, cv_3(l, x, y, b), cv_2(l, x, y, b))), h3)
  +f_hd = cvle(Nat.mul(2n, b), Nat.add(y, x), L{0n, 0n, 0n, 0n, 2n}, L{0n, 0n, 1n, 1n, 0n}, v,
    cv_mul(2n, b, L{0n, 0n, 0n, 0n, 1n}, v, cv_4(l, x, y, b)),
    cv_add(y, x, L{0n, 0n, 0n, 1n, 0n}, L{0n, 0n, 1n, 0n, 0n}, v, cv_3(l, x, y, b), cv_2(l, x, y, b)), hd)
  +f_h6 = cvle(y, Nat.mul(3n, x), L{0n, 0n, 0n, 1n, 0n}, L{0n, 0n, 3n, 0n, 0n}, v,
    cv_3(l, x, y, b),
    cv_mul(3n, x, L{0n, 0n, 1n, 0n, 0n}, v, cv_2(l, x, y, b)), h6)
  contra(L{4n, 3n, 9n, 2n, 2n}, L{0n, 3n, 8n, 2n, 1n}, v,
    comb(L{3n, 0n, 9n, 0n, 0n}, L{0n, 3n, 0n, 0n, 0n}, L{1n, 3n, 0n, 2n, 2n}, L{0n, 0n, 8n, 2n, 1n}, v, scale(3n, L{1n, 0n, 3n, 0n, 0n}, L{0n, 1n, 0n, 0n, 0n}, v, f_ng),
    comb(L{1n, 3n, 0n, 0n, 0n}, L{0n, 0n, 1n, 1n, 1n}, L{0n, 0n, 0n, 2n, 2n}, L{0n, 0n, 7n, 1n, 0n}, v, f_h3,
    comb(L{0n, 0n, 0n, 0n, 2n}, L{0n, 0n, 1n, 1n, 0n}, L{0n, 0n, 0n, 2n, 0n}, L{0n, 0n, 6n, 0n, 0n}, v, f_hd,
    scale(2n, L{0n, 0n, 0n, 1n, 0n}, L{0n, 0n, 3n, 0n, 0n}, v, f_h6)))), {==})

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=LE
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=Lin
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=Vs
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=comb
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=contra
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=cv_1
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=cv_2
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=cv_3
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=cv_4
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=cv_add
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=cv_c
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=cv_mul
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=cvle
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/nat_order.bend&name=scale