PROOF.len_drow: def of bendtorch@1.3.0.0
Import: import bendtorch@1.3.0.0/PROOF.bend as PROOF
Lines 173-179 of bendtorch@1.3.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch@1.3.0.0/PROOF.bend&start_line=173&end_line=179

import Base
import bendtorch@1.3.0.0/main.bend as T
import bend-ml-nat-lemmas@0.1.2.0/main.bend as NL

# drow's row has the current dot, the m after it, and acc: 1 + m + |acc| numbers
def len_drow(m: Nat, +hd: Nat, +ia: U32, +ib: U32, +bs: U32, +acc: List<&2, F32>, r: T.D2) -> {List.length(&2, F32, T.dr_row(T.drow(m, hd, ia, ib, bs, acc, r))) == Nat.add(1n+m, List.length(&2, F32, acc)) : Nat}:
  match m r:
    case 0n T.D2{a, b, +s}:
      Equal.trans(Nat, List.length(&2, F32, T.rcat(s <> acc, Nil{})), Nat.add(1n+List.length(&2, F32, acc), 0n), 1n+List.length(&2, F32, acc), len_rcat(s <> acc, Nil{}), NL.add_zero(1n+List.length(&2, F32, acc)))
    case 1n++p T.D2{a, b, +s}:
      Equal.trans(Nat, List.length(&2, F32, T.dr_row(T.drow(p, hd, ia, (ib + bs : U32), bs, s <> acc, T.dot0(hd, ia, (ib + bs : U32), 1, 1, a, b)))), Nat.add(1n+p, 1n+List.length(&2, F32, acc)), 2n+Nat.add(p, List.length(&2, F32, acc)), len_drow(p, hd, ia, (ib + bs : U32), bs, s <> acc, T.dot0(hd, ia, (ib + bs : U32), 1, 1, a, b)), Equal.cong(Nat, Nat, z => 1n+z, Nat.add(p, 1n+List.length(&2, F32, acc)), 1n+Nat.add(p, List.length(&2, F32, acc)), Equal.sym(Nat, 1n+Nat.add(p, List.length(&2, F32, acc)), Nat.add(p, 1n+List.length(&2, F32, acc)), NL.add_succ(p, List.length(&2, F32, acc)))))

Uses (18):
  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=List.length
  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=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  https://jend.leeeet.dev/definition.txt?path=bend-ml-nat-lemmas@0.1.2.0/main.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=bend-ml-nat-lemmas@0.1.2.0/main.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/PROOF.bend&name=len_rcat
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=D2
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=dot0
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=dr_row
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=drow
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=rcat