PROOF.g_lenu: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 500-506 of bend-osdev-bytes@0.1.1.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&start_line=500&end_line=506

import Base
import bend-osdev-bytes@0.1.1.0/bytes.bend as B
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

def g_lenu(+xs: List<&2, U32>, +n: Nat) -> {B.len.go(xs, n) == Nat.add(B.len(xs), n) : Nat}:
  match xs:
    case Nil{}:
      {==}
    case Con{h, t}:
      Equal.trans(Nat, B.len.go(t, 1n+n), Nat.add(B.len(t), 1n+n), 1n+Nat.add(B.len(t), n),
        g_lenu(t, 1n+n), UL.nat_add_succ(B.len(t), n))

Uses (8):
  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=U32
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=len
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=len.go
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_succ