NatOrder.le_lt_trans: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 281-295 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=281&end_line=295

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

def le_lt_trans(+a: Nat,+b: Nat,+c: Nat,ab: {Nat.is_le(a,b) == True{} : Bool},bc: {Nat.is_lt(b,c) == True{} : Bool}) -> {Nat.is_lt(a,
    c) == True{} : Bool}:
  match a b c:
    case 0n 0n 0n:
      Empty.absurd({Nat.is_lt(0n,0n) == True{} : Bool},WordEncoding.false_true(bc))
    case 0n 1n+b 0n:
      Empty.absurd({Nat.is_lt(0n,0n) == True{} : Bool},WordEncoding.false_true(bc))
    case 0n b 1n+c:
      {==}
    case 1n+a 0n c:
      Empty.absurd({Nat.is_lt(1n+a,c) == True{} : Bool},WordEncoding.false_true(ab))
    case 1n+a 1n+b 0n:
      Empty.absurd({Nat.is_lt(1n+a,0n) == True{} : Bool},WordEncoding.false_true(bc))
    case 1n+a 1n+b 1n+c:
      le_lt_trans(a,b,c,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=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true