SignedPROOF.size_beyond: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend as SignedPROOF
Lines 420-436 of bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend&start_line=420&end_line=436

import Base
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/signed.bend as Signed

# The two branches of a single Inferred size with a nonzero product p: p at
# most the count divides; p past it leaves an empty input's size 0 and
# refuses any other.
def size_beyond(+count: Nat, +extents: List<&2, Signed.Extent>, +rest: Nat, +quotient: Nat,
  exact: {Nat.mul(quotient, 1n+rest) == count : Nat}, past: {Nat.is_le(1n+rest, count) == False{} : Bool}) ->
  {Signed.beyond(count, extents) == Done{Signed.filled(extents, U32.from_nat(quotient))} : Result<&2, &2, Signed.Error, List<&2, U32>>}:
  match quotient:
    case 0n:
      %exact : {Signed.beyond(_, extents) == Done{Signed.filled(extents, U32.from_nat(0n))} : Result<&2, &2, Signed.Error, List<&2, U32>>}
      {==}
    case 1n+q:
      Empty.absurd({Signed.beyond(count, extents) == Done{Signed.filled(extents, U32.from_nat(1n+q))} : Result<&2, &2, Signed.Error, List<&2, U32>>},
        Arith.clash_true(Equal.trans(Bool, True{}, Nat.is_le(1n+rest, count), False{},
          Equal.trans(Bool, True{}, Nat.is_le(1n+rest, Nat.add(1n+rest, Nat.mul(q, 1n+rest))), Nat.is_le(1n+rest, count),
            Equal.sym(Bool, Nat.is_le(1n+rest, Nat.add(1n+rest, Nat.mul(q, 1n+rest))), True{}, le_add(1n+rest, Nat.mul(q, 1n+rest))),
            Equal.cong(Nat, Bool, x => Nat.is_le(1n+rest, x), Nat.add(1n+rest, Nat.mul(q, 1n+rest)), count, exact)),
          past)))

Uses (19):
  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.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  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_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  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/arith.bend&name=clash_true
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed.bend&name=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed.bend&name=Extent
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed.bend&name=beyond
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed.bend&name=filled
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend&name=le_add