PROOF.len_rcat: def of bendtorch@1.3.0.0
Import: import bendtorch@1.3.0.0/PROOF.bend as PROOF
Lines 165-171 of bendtorch@1.3.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch@1.3.0.0/PROOF.bend&start_line=165&end_line=171

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

# xs reversed onto acc has the length of both
def len_rcat(+xs: List<&2, F32>, +acc: List<&2, F32>) -> {List.length(&2, F32, T.rcat(xs, acc)) == Nat.add(List.length(&2, F32, xs), List.length(&2, F32, acc)) : Nat}:
  match xs:
    case Nil{}:
      {==}
    case Con{+x, +t}:
      Equal.trans(Nat, List.length(&2, F32, T.rcat(t, x <> acc)), Nat.add(List.length(&2, F32, t), 1n+List.length(&2, F32, acc)), 1n+Nat.add(List.length(&2, F32, t), List.length(&2, F32, acc)), len_rcat(t, x <> acc), Equal.sym(Nat, 1n+Nat.add(List.length(&2, F32, t), List.length(&2, F32, acc)), Nat.add(List.length(&2, F32, t), 1n+List.length(&2, F32, acc)), NL.add_succ(List.length(&2, F32, t), List.length(&2, F32, acc))))

Uses (9):
  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=bend-ml-nat-lemmas@0.1.2.0/main.bend&name=add_succ
  https://jend.leeeet.dev/definition.txt?path=bendtorch@1.3.0.0/main.bend&name=rcat