SlicePROOF.source_at: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend as SlicePROOF
Lines 736-755 of bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend&start_line=736&end_line=755

import Base
import bendtorch-core@0.1.0.0/src/tensor/slice.bend as Slice
import bendtorch-core@0.1.0.0/src/tensor/slice_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend as BatchedProof

# The forward cell (o, k, r) reads input cell (o, start + k * step, r).
def source_at(+outer: Nat, +extent: Nat, +inner: Nat, +start: Nat, +step: Nat, +length: Nat, +o: Nat, +k: Nat, +r: Nat,
  +k_below: {Nat.is_lt(k, length) == True{} : Bool}, +r_below: {Nat.is_lt(r, inner) == True{} : Bool}) ->
  {Slice.source(Slice.Plan{outer, extent, inner, start, step, length}, Laws.position(length, inner, o, k, r)) ==
    Laws.position(extent, inner, o, Nat.add(start, Nat.mul(k, step)), r) : Nat}:
  +row = Nat.add(Nat.mul(o, length), k)
  +pos = Laws.position(length, inner, o, k, r)
  %Equal.sym(Nat, Nat.div(pos, inner), row, BatchedProof.div_exact(row, inner, r, r_below)) :
    {Nat.add(Nat.mul(Nat.add(Nat.mul(Nat.div(_, length), extent), Nat.add(start, Nat.mul(Nat.mod(_, length), step))), inner), Nat.mod(pos, inner)) ==
      Laws.position(extent, inner, o, Nat.add(start, Nat.mul(k, step)), r) : Nat}
  %Equal.sym(Nat, Nat.mod(pos, inner), r, BatchedProof.mod_exact(row, inner, r, r_below)) :
    {Nat.add(Nat.mul(Nat.add(Nat.mul(Nat.div(row, length), extent), Nat.add(start, Nat.mul(Nat.mod(row, length), step))), inner), _) ==
      Laws.position(extent, inner, o, Nat.add(start, Nat.mul(k, step)), r) : Nat}
  %Equal.sym(Nat, Nat.div(row, length), o, BatchedProof.div_exact(o, length, k, k_below)) :
    {Nat.add(Nat.mul(Nat.add(Nat.mul(_, extent), Nat.add(start, Nat.mul(Nat.mod(row, length), step))), inner), r) ==
      Laws.position(extent, inner, o, Nat.add(start, Nat.mul(k, step)), r) : Nat}
  %Equal.sym(Nat, Nat.mod(row, length), k, BatchedProof.mod_exact(o, length, k, k_below)) :
    {Nat.add(Nat.mul(Nat.add(Nat.mul(o, extent), Nat.add(start, Nat.mul(_, step))), inner), r) ==
      Laws.position(extent, inner, o, Nat.add(start, Nat.mul(k, step)), r) : Nat}
  {==}

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.div
  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.mod
  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/tensor/batched_matmul_PROOF.bend&name=div_exact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend&name=mod_exact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=Plan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=source
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_LAWS.bend&name=position