GatherPROOF.entry_read: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend as GatherPROOF
Lines 393-405 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=393&end_line=405

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/gather_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/parallel_proofs.bend as Generic

# The entry the cell reads, as the laws name it, rewritten to the code's.
def entry_read(+depth: Nat, +path: Model.Path(depth), +base: Nat, +kind: Gather.Lookup, +outer: Nat, +rows: Nat, +inner: Nat, +count: Nat,
  +o: Nat, +k: Nat, +r: Nat, +k_below: {Nat.is_lt(k, count) == True{} : Bool}, +r_below: {Nat.is_lt(r, inner) == True{} : Bool},
  +at: {Nat.add(Model.offset(depth, path), base) == Laws.position(count, inner, o, k, r) : Nat}, +di: Nat, -I: Array<U32>, +j: U32,
  -read: {Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(Laws.entry_at(kind, count, inner, o, k, r)))) == Some{j} : Maybe<&2, U32>}) ->
  Generic.Fact<{Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, Nat.add(Model.offset(depth, path), base))))) == Some{j} : Maybe<&2, U32>}>:
  Generic.Fact{Equal.trans(Maybe<&2, U32>, Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, Nat.add(Model.offset(depth, path), base))))),
    Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(Laws.entry_at(kind, count, inner, o, k, r)))), Some{j},
    Equal.cong(Nat, Maybe<&2, U32>, e => Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(e))), Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, Nat.add(Model.offset(depth, path), base)), Laws.entry_at(kind, count, inner, o, k, r),
      Equal.trans(Nat, Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, Nat.add(Model.offset(depth, path), base)), Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, Laws.position(count, inner, o, k, r)), Laws.entry_at(kind, count, inner, o, k, r),
        Equal.cong(Nat, Nat, x => Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, x), Nat.add(Model.offset(depth, path), base), Laws.position(count, inner, o, k, r), at),
        entry_at(kind, outer, rows, inner, count, o, k, r, k_below, r_below))),
    read)}

Uses (21):
  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.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/model.bend&name=Path
  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/model.bend&name=offset
  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/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=entry
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend&name=entry_at
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend&name=position
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&name=entry_at
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/parallel_proofs.bend&name=Fact