MatmulParallelProof.le_trans: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend as MatmulParallelProof
Lines 198-208 of bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend&start_line=198&end_line=208

import Base
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith

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