NatOrder.transitive: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 169-183 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=169&end_line=183

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

def transitive(+a: Nat,+b: Nat,+c: Nat,ab: {Nat.is_le(a,b) == True{} : Bool},bc: {Nat.is_le(b,c) == True{} : Bool}) -> {Nat.is_le(a,
    c) == True{} : Bool}:
  match a:
    case 0n:
      zero_le(c)
    case 1n+ +p:
      match b:
        case 0n:
          Empty.absurd({Nat.is_le(1n+p,c) == True{} : Bool},WordEncoding.false_true(ab))
        case 1n+ +q:
          match c:
            case 0n:
              Empty.absurd({Nat.is_le(1n+p,0n) == True{} : Bool},WordEncoding.false_true(bc))
            case 1n+r:
              transitive(p,q,r,ab,bc)

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