Float.max_l: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend as Float
Lines 166-175 of bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&start_line=166&end_line=175

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

def max_l(+a: Nat, +b: Nat, +h: {Nat.is_le(b, a) == True{} : Bool}) -> {Nat.max(a, b) == a : Nat}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+bp:
      Empty.absurd({Nat.max(0n, 1n+bp) == 0n : Nat}, L.false_true(h))
    case 1n+ap 0n:
      {==}
    case 1n+ap 1n+bp:
      Equal.cong(Nat, Nat, z => 1n+z, Nat.max(ap, bp), ap, max_l(ap, bp, h))

Uses (7):
  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.max
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=false_true