Lemire.min_succ: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend as Lemire
Lines 213-223 of bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&start_line=213&end_line=223

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

# min(N + 1, C) = min(N, C) + [N < C]
def min_succ(+n: Nat, +c: Nat) -> {Nat.min(1n+n, c) == Nat.add(Nat.min(n, c), b2n(Nat.is_lt(n, c))) : Nat}:
  match n c:
    case _ 0n:
      %Equal.sym(Nat, Nat.min(n, 0n), 0n, min_zero(n)) : {0n == Nat.add(_, b2n(Nat.is_lt(n, 0n))) : Nat}
      %Equal.sym(Bool, Nat.is_lt(n, 0n), False{}, N.not_lt_zero(n)) : {0n == Nat.add(0n, b2n(_)) : Nat}
      {==}
    case 0n 1n+q:
      {==}
    case 1n+p 1n+q:
      Equal.cong(Nat, Nat, z => 1n+z, Nat.min(1n+p, q), Nat.add(Nat.min(p, q), b2n(Nat.is_lt(p, q))), min_succ(p, q))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.min
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=not_lt_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&name=b2n
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&name=min_zero