NatOrder.sub_le: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 202-211 of stelliferous@0.0.2.0/proofs/nat_order.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&start_line=202&end_line=211

import Base

def sub_le(+a: Nat,+b: Nat) -> {Nat.is_le(Nat.sub(a,b),a) == True{} : Bool}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+b:
      {==}
    case 1n+ +a 0n:
      reflexive(1n+a)
    case 1n+ +a 1n+ +b:
      successor(Nat.sub(a,b),a,sub_le(a,b))

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.sub
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=reflexive
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&name=successor