Fact.choose_one_right: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/fact.bend as Fact
Lines 128-135 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/fact.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/fact.bend&start_line=128&end_line=135

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/spec/math/natural.bend as S

# C(n, 1) == n
def choose_one_right(+n: Nat) -> {S.choose(n, 1n) == n : Nat}:
  match n:
    case 0n:
      {==}
    case 1n+ +m:
      %Equal.sym(Nat, S.choose(m, 0n), 1n, choose_zero_right(m)) : {Nat.add(_, S.choose(m, 1n)) == 1n+m : Nat}
      N.succ_cong(S.choose(m, 1n), m, choose_one_right(m))

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=succ_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/fact.bend&name=choose_zero_right
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/math/natural.bend&name=choose