Nat.min_right: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 544-553 of bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&start_line=544&end_line=553

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

def min_right(+a: Nat, +b: Nat, +h: {Nat.is_lt(a, b) == False{} : Bool}) -> {Nat.min(a, b) == b : Nat}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+bp:
      Empty.absurd({Nat.min(0n, 1n+bp) == 1n+bp : Nat}, zero_succ(0n, Equal.sym(Nat, 1n, 0n, Equal.cong(Bool, Nat, c => S.bit_value(c), True{}, False{}, h))))
    case 1n+ap 0n:
      {==}
    case 1n+ap 1n+bp:
      succ_cong(Nat.min(ap, bp), bp, min_right(ap, bp, h))

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=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=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.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/lemmas/spec/numeric.bend&name=bit_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=succ_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=zero_succ