PROOF.off.min_le: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 807-815 of bend-osdev-bytes@0.1.1.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&start_line=807&end_line=815

import Base

# n <= k: min(n, k) == n
def off.min_le(+n: Nat, +k: Nat) -> {Nat.is_le(n, k) == True{} : Bool} -> {Nat.min(n, k) == n : Nat}:
  match n k:
    case 0n _:
      h => {==}
    case 1n+p 0n:
      h => off.no({Nat.min(1n+p, 0n) == 1n+p : Nat}, h)
    case 1n+p 1n+q:
      h => Equal.cong(Nat, Nat, x => 1n+x, Nat.min(p, q), p, off.min_le(p, q, h))

Uses (6):
  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=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-osdev-bytes@0.1.1.0/PROOF.bend&name=off.no