ReduceFiberProof.walk_left_row: 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 377-396 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=377&end_line=396

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend as Nats
import bendtorch-core@0.1.0.0/src/shape/broadcast_proofs.bend as Broadcast
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend as MatrixIndex

def walk_left_row(+lh: Nat, +rh: Nat, +oh: Nat, axis: Shape.Axis<lh, rh, oh>, +size: Nat, +d: Nat, +w: Nat,
  d_below: {Nat.is_lt(d, oh) == True{} : Bool}, w_below: {Nat.is_lt(w, size) == True{} : Bool}) ->
  {Nat.is_lt(Nat.add(Nat.mul(Shape.broadcast_index(lh, size), d), w), Nat.mul(lh, size)) == True{} : Bool}:
  match lh:
    case 0n:
      Empty.absurd({Nat.is_lt(Nat.add(Nat.mul(size, d), w), 0n) == True{} : Bool},
        Arith.lt_zero(d,
          %axis_zero(rh, oh, axis) : {Nat.is_lt(d, _) == True{} : Bool}
          d_below))
    case 1n+k:
      match k:
        case 0n:
          %Equal.sym(Nat, Nat.add(size, 0n), size, Broadcast.add_zero(size)) : {Nat.is_lt(w, _) == True{} : Bool}
          w_below
        case 1n+j:
          %Nats.mul_comm(d, size) : {Nat.is_lt(Nat.add(_, w), Nat.mul(2n+j, size)) == True{} : Bool}
          MatrixIndex.lt_mul_add(d, 2n+j, w, size,
            %axis_kept(j, rh, oh, axis) : {Nat.is_lt(d, _) == True{} : Bool}
            d_below,
            w_below)

Uses (15):
  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=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  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=axis_kept
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fiber_proof.bend&name=axis_zero
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/broadcast_proofs.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Axis
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=broadcast_index
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend&name=mul_comm
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=lt_zero
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=lt_mul_add