NatExtrema.minimum_when_ordered: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_extrema.bend as NatExtrema
Lines 31-36 of stelliferous@0.0.2.0/proofs/nat_extrema.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/nat_extrema.bend&start_line=31&end_line=36

import Base
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding

def minimum_when_ordered(+left: Nat,+right: Nat,ordered: {Nat.is_le(left,right) == True{} : Bool}) -> {Nat.min(left,right) == left : Nat}:
  match left right:
    case 0n right: {==}
    case 1n+left 0n: Empty.absurd({Nat.min(1n+left,0n) == 1n+left : Nat},WordEncoding.false_true(ordered))
    case 1n+ +left 1n+ +right:
      Equal.cong(Nat,Nat,n => 1n+n,Nat.min(left,right),left,minimum_when_ordered(left,right,ordered))

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.min
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true