Lemire.min_le: 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 271-278 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=271&end_line=278

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L

def min_le(+n: Nat, +c: Nat, +h: {Nat.is_le(c, n) == True{} : Bool}) -> {Nat.min(n, c) == c : Nat}:
  match n c:
    case _ 0n:
      min_zero(n)
    case 0n 1n+q:
      Empty.absurd({Nat.min(0n, 1n+q) == 1n+q : Nat}, L.false_true(h))
    case 1n+p 1n+q:
      Equal.cong(Nat, Nat, z => 1n+z, Nat.min(p, q), q, min_le(p, q, h))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  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/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/lemire.bend&name=min_zero