PROOF.b_par_fin_f: def of bendtorch@1.3.0.0
Import: import bendtorch@1.3.0.0/PROOF.bend as PROOF
Lines 807-814 of bendtorch@1.3.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch@1.3.0.0/PROOF.bend&start_line=807&end_line=814

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

# the law: the b_treef gives what fleaf, the loop over the sequences one after another, gives
def b_par_fin_f(-d: Nat, -gs: T.Halves<T.BG>, -n: Nat, +h: Nat, +dm: T.Dm, -ys: List<&1, T.BG>, +sy: {ys == T.hcat(T.BG, gs) : List<&1, T.BG>}, f: {T.bpar_full(d, gs, n, h, dm) == b_ffmap(h, dm, T.hcat(T.BG, gs)) : List<&1, T.DB>}, r: b_L1RF<h, dm, ys, Nil{}>) -> {T.bpar_full(d, gs, n, h, dm) == T.bleaf_full(T.hcat(T.BG, gs), h, dm, Nil{}) : List<&1, T.DB>}:
  match r:
    case b_L1RF{ys2, s2, fl}:
      Equal.trans(List<&1, T.DB>, T.bpar_full(d, gs, n, h, dm), b_ffmap(h, dm, T.hcat(T.BG, gs)), T.bleaf_full(T.hcat(T.BG, gs), h, dm, Nil{}), f,
        Equal.sym(List<&1, T.DB>, T.bleaf_full(T.hcat(T.BG, gs), h, dm, Nil{}), b_ffmap(h, dm, T.hcat(T.BG, gs)),
          Equal.trans(List<&1, T.DB>, T.bleaf_full(T.hcat(T.BG, gs), h, dm, Nil{}), T.bleaf_full(ys, h, dm, Nil{}), b_ffmap(h, dm, T.hcat(T.BG, gs)), Equal.cong(List<&1, T.BG>, List<&1, T.DB>, z => T.bleaf_full(z, h, dm, Nil{}), T.hcat(T.BG, gs), ys, Equal.sym(List<&1, T.BG>, ys, T.hcat(T.BG, gs), sy)),
            Equal.trans(List<&1, T.DB>, T.bleaf_full(ys, h, dm, Nil{}), b_ffmap(h, dm, ys), b_ffmap(h, dm, T.hcat(T.BG, gs)), fl, Equal.cong(List<&1, T.BG>, List<&1, T.DB>, z => b_ffmap(h, dm, z), ys, T.hcat(T.BG, gs), sy)))))

Uses (14):
  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=bendtorch@1.3.0.0/PROOF.bend&name=b_L1RF
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/PROOF.bend&name=b_ffmap
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=BG
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=DB
  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=Halves
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=bleaf_full
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=bpar_full
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=hcat