ReduceFiberProof.mul_le_mono: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend as ReduceFiberProof
Lines 137-145 of bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend&start_line=137&end_line=145

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

def mul_le_mono(+a: Nat, +q: Nat, +size: Nat, h: {Nat.is_le(a, q) == True{} : Bool}) ->
  {Nat.is_le(Nat.mul(a, size), Nat.mul(q, size)) == True{} : Bool}:
  match a q:
    case 0n q:
      Arith.le_zero(Nat.mul(q, size))
    case 1n+p 0n:
      Empty.absurd({Nat.is_le(Nat.mul(1n+p, size), 0n) == True{} : Bool}, Arith.clash(h))
    case 1n+p 1n+r:
      le_add_cong(size, Nat.mul(p, size), Nat.mul(r, size), mul_le_mono(p, r, size, h))

Uses (8):
  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.mul
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend&name=le_add_cong
  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