Misc.min_eq_l: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/natural/misc.bend as Misc
Lines 67-74 of bend-collections-laws-math@1.0.0.0/proofs/math/natural/misc.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/misc.bend&start_line=67&end_line=74

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

def min_eq_l(+y: Nat, +hi: Nat, +h: {Nat.is_le(y, hi) == True{} : Bool}) -> {Nat.min(y, hi) == y : Nat}:
  match y hi:
    case 0n h0:
      {==}
    case 1n+yp 0n:
      Empty.absurd({Nat.min(1n+yp, 0n) == 1n+yp : Nat}, L.false_true(h))
    case 1n+ +yp 1n+ +hp:
      N.succ_cong(Nat.min(yp, hp), yp, min_eq_l(yp, hp, 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=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/lib/nat.bend&name=succ_cong