PROOF.par_fin: def of bendtorch@1.3.0.0
Import: import bendtorch@1.3.0.0/PROOF.bend as PROOF
Lines 423-430 of bendtorch@1.3.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch@1.3.0.0/PROOF.bend&start_line=423&end_line=430

import Base
import bendtorch@1.3.0.0/main.bend as T

# the law: the tree gives what fleaf, the loop over the sequences one after another, gives
def par_fin(-d: Nat, -gs: T.Halves<T.FS>, -n: Nat, +h: Nat, +dm: T.Dm, -ys: List<&1, T.FS>, +sy: {ys == T.hcat(T.FS, gs) : List<&1, T.FS>}, f: {T.fpar(d, gs, n, h, dm) == fmap(h, dm, T.hcat(T.FS, gs)) : List<&1, Array<F32>>}, r: L1R<h, dm, ys, Nil{}>) -> {T.fpar(d, gs, n, h, dm) == T.fleaf(T.hcat(T.FS, gs), h, dm, Nil{}) : List<&1, Array<F32>>}:
  match r:
    case L1R{ys2, s2, fl}:
      Equal.trans(List<&1, Array<F32>>, T.fpar(d, gs, n, h, dm), fmap(h, dm, T.hcat(T.FS, gs)), T.fleaf(T.hcat(T.FS, gs), h, dm, Nil{}), f,
        Equal.sym(List<&1, Array<F32>>, T.fleaf(T.hcat(T.FS, gs), h, dm, Nil{}), fmap(h, dm, T.hcat(T.FS, gs)),
          Equal.trans(List<&1, Array<F32>>, T.fleaf(T.hcat(T.FS, gs), h, dm, Nil{}), T.fleaf(ys, h, dm, Nil{}), fmap(h, dm, T.hcat(T.FS, gs)), Equal.cong(List<&1, T.FS>, List<&1, Array<F32>>, z => T.fleaf(z, h, dm, Nil{}), T.hcat(T.FS, gs), ys, Equal.sym(List<&1, T.FS>, ys, T.hcat(T.FS, gs), sy)),
            Equal.trans(List<&1, Array<F32>>, T.fleaf(ys, h, dm, Nil{}), fmap(h, dm, ys), fmap(h, dm, T.hcat(T.FS, gs)), fl, Equal.cong(List<&1, T.FS>, List<&1, Array<F32>>, z => fmap(h, dm, z), ys, T.hcat(T.FS, gs), sy)))))

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  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=F32
  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=bendtorch@1.3.0.0/PROOF.bend&name=L1R
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/PROOF.bend&name=fmap
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=Dm
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=FS
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=Halves
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=fleaf
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=fpar
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=hcat