Arith.lt_le_trans: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
Lines 257-279 of bendtorch-core@0.1.0.0/src/storage/arith.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&start_line=257&end_line=279

import Base

def lt_le_trans(+a: Nat, +b: Nat, +c: Nat, ab: {Nat.is_lt(a, b) == True{} : Bool},
  bc: {Nat.is_le(b, c) == True{} : Bool}) -> {Nat.is_lt(a, c) == True{} : Bool}:
  match a:
    case 0n:
      match b:
        case 0n:
          Empty.absurd({Nat.is_lt(0n, c) == True{} : Bool}, clash(ab))
        case 1n+q:
          match c:
            case 0n:
              Empty.absurd({Nat.is_lt(0n, 0n) == True{} : Bool}, clash(bc))
            case 1n+r:
              {==}
    case 1n+p:
      match b:
        case 0n:
          Empty.absurd({Nat.is_lt(1n+p, c) == True{} : Bool}, clash(ab))
        case 1n+q:
          match c:
            case 0n:
              Empty.absurd({Nat.is_lt(1n+p, 0n) == True{} : Bool}, clash(bc))
            case 1n+r:
              lt_le_trans(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=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=clash