GatherPROOF.compared_is: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend as GatherPROOF
Lines 481-489 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=481&end_line=489

import Base
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/storage/refinement.bend as Refinement
import bendtorch-core@0.1.0.0/src/tensor/gather.bend as Gather
import bendtorch-core@0.1.0.0/src/tensor/parallel_proofs.bend as Generic

def compared_is(+i: Nat, +at: Nat, +slot: Nat, +acc: F32, +dg: Nat, -G: Array<F32>, +di: Nat, -I: Array<U32>, pair: Array<U32> & U32,
  -kept: {Refinement.first(U32, pair) == I : Array<U32>},
  -seen: {Some{Refinement.second(U32, pair)} == Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(slot))) : Maybe<&2, U32>},
  -valid: Model.Balanced(F32, dg, G)) ->
  Generic.Fact<Stepped<dg, G, di, I, i, at, slot, acc, Gather.compared(i, at, acc, G, pair)>>:
  (index, +j) = pair
  summed_is(i, at, slot, acc, dg, G, di, I, index, j, kept,
    Equal.sym(Maybe<&2, U32>, Some{j}, Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(slot))), seen),
    Nat.is_eq(U32.to_nat(j), i), {==}, valid)

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=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=Maybe
  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_eq
  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=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/model.bend&name=Balanced
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/model.bend&name=observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/refinement.bend&name=first
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/refinement.bend&name=route
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/refinement.bend&name=second
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=compared
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&name=Stepped
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&name=summed_is
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/parallel_proofs.bend&name=Fact