GatherPROOF.scattered_at: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend as GatherPROOF
Lines 610-626 of bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&start_line=610&end_line=626

import Base
import bendtorch-core@0.1.0.0/src/tensor/gather.bend as Gather
import bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend as BatchedProof

# Input cell (o, i, r) runs the sum of (o, i, r).
def scattered_at(+kind: Gather.Lookup, +outer: Nat, +rows: Nat, +inner: Nat, +count: Nat, +o: Nat, +i: Nat, +r: Nat,
  +i_below: {Nat.is_lt(i, rows) == True{} : Bool}, +r_below: {Nat.is_lt(r, inner) == True{} : Bool}, -state: Array<F32> & Array<U32>) ->
  {Gather.scattered(Gather.Plan{kind, outer, rows, inner, count}, Laws.position(rows, inner, o, i, r), state) == Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, i, r, count, 0n, (0.0, state)) : F32 & (Array<F32> & Array<U32>)}:
  +row = Nat.add(Nat.mul(o, rows), i)
  +pos = Laws.position(rows, inner, o, i, r)
  %Equal.sym(Nat, Nat.div(pos, inner), row, BatchedProof.div_exact(row, inner, r, r_below)) :
    {Gather.added(Gather.Plan{kind, outer, rows, inner, count}, Nat.div(_, rows), Nat.mod(_, rows), Nat.mod(pos, inner), count, 0n, (0.0, state)) ==
      Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, i, r, count, 0n, (0.0, state)) : F32 & (Array<F32> & Array<U32>)}
  %Equal.sym(Nat, Nat.mod(pos, inner), r, BatchedProof.mod_exact(row, inner, r, r_below)) :
    {Gather.added(Gather.Plan{kind, outer, rows, inner, count}, Nat.div(row, rows), Nat.mod(row, rows), _, count, 0n, (0.0, state)) ==
      Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, i, r, count, 0n, (0.0, state)) : F32 & (Array<F32> & Array<U32>)}
  %Equal.sym(Nat, Nat.div(row, rows), o, BatchedProof.div_exact(o, rows, i, i_below)) :
    {Gather.added(Gather.Plan{kind, outer, rows, inner, count}, _, Nat.mod(row, rows), r, count, 0n, (0.0, state)) == Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, i, r, count, 0n, (0.0, state)) : F32 & (Array<F32> & Array<U32>)}
  %Equal.sym(Nat, Nat.mod(row, rows), i, BatchedProof.mod_exact(o, rows, i, i_below)) :
    {Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, _, r, count, 0n, (0.0, state)) == Gather.added(Gather.Plan{kind, outer, rows, inner, count}, o, i, r, count, 0n, (0.0, state)) : F32 & (Array<F32> & Array<U32>)}
  {==}

Uses (20):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  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=F32
  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=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  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/gather.bend&name=Lookup
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=Plan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=added
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=scattered
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend&name=position