NatExtrema.maximum_choice: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_extrema.bend as NatExtrema
Lines 22-29 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=22&end_line=29

import Base

def maximum_choice(+left: Nat,+right: Nat) -> {Nat.max(left,right) == Bool.pick(Nat,Nat.is_lt(left,right),right,left) : Nat}:
  match left right:
    case 0n 0n: {==}
    case 0n 1n+right: {==}
    case 1n+left 0n: {==}
    case 1n+ +left 1n+ +right:
      Equal.trans(Nat,1n+Nat.max(left,right),1n+Bool.pick(Nat,Nat.is_lt(left,right),right,left),Bool.pick(Nat,Nat.is_lt(left,right),1n+right,1n+left),
        Equal.cong(Nat,Nat,n => 1n+n,Nat.max(left,right),Bool.pick(Nat,Nat.is_lt(left,right),right,left),maximum_choice(left,right)),successor_pick(Nat.is_lt(left,right),right,left))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.pick
  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.trans
  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.max
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_extrema.bend&name=successor_pick