Fixprime.zc: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend as Fixprime
Lines 47-54 of bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&start_line=47&end_line=54

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend as SF
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD

def zc(+one: Nat, +h1: {one == 1n : Nat}, +r: Nat, +x: Nat, +c: Bool, +e: {Nat.add(r, C.shift(32n, WD.bo(c, one))) == Nat.add(x, 1n) : Nat}, +hx: {C.fits(32n, x) == True{} : Bool}) -> {SF.bn(Nat.is_eq(r, 0n)) == WD.bo(c, one) : Nat}:
  match c:
    case True{}:
      zc_t(one, h1, r, x, e, hx)
    case False{}:
      +er = Equal.trans(Nat, r, Nat.add(r, 0n), 1n+x, Equal.sym(Nat, Nat.add(r, 0n), r, N.add_zero(r)), Equal.trans(Nat, Nat.add(r, 0n), Nat.add(x, 1n), 1n+x, e, N.add_comm(x, 1n)))
      %Equal.sym(Nat, r, 1n+x, er) : {SF.bn(Nat.is_eq(_, 0n)) == 0n : Nat}
      {==}

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend&name=bo
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/number/fixprime.bend&name=zc_t
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=fits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=shift
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/fixed.bend&name=bn