PROOF.sp.nonempty: def of bend-osdev-cipher-modes@0.1.0.0
Import: import bend-osdev-cipher-modes@0.1.0.0/PROOF.bend as PROOF
Lines 621-688 of bend-osdev-cipher-modes@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&start_line=621&end_line=688

import Base
import bend-osdev-bytes@0.1.0.0/bytes.bend as B
import bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend as M

# a byte string of at least 16 bytes has a first block
def sp.nonempty(ys: List<&2, U32>) -> {Nat.is_le(16n, B.len(ys)) == True{} : Bool} -> {Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(ys)))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(ys))))} == M.cm.split.blocks(M.cm.split(B.mask(ys))) : List<&2, M.CmBlock>}:
  match ys:
    case Nil{}:
      h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Nil{})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Nil{}))))} == M.cm.split.blocks(M.cm.split(B.mask(Nil{}))) : List<&2, M.CmBlock>}, h)
    case Con{+y0, +r0}:
      match r0:
        case Nil{}:
          h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Nil{}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Nil{}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Nil{}}))) : List<&2, M.CmBlock>}, h)
        case Con{+y1, +r1}:
          match r1:
            case Nil{}:
              h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Nil{}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Nil{}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Nil{}}}))) : List<&2, M.CmBlock>}, h)
            case Con{+y2, +r2}:
              match r2:
                case Nil{}:
                  h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Nil{}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Nil{}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Nil{}}}}))) : List<&2, M.CmBlock>}, h)
                case Con{+y3, +r3}:
                  match r3:
                    case Nil{}:
                      h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Nil{}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Nil{}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Nil{}}}}}))) : List<&2, M.CmBlock>}, h)
                    case Con{+y4, +r4}:
                      match r4:
                        case Nil{}:
                          h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Nil{}}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Nil{}}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Nil{}}}}}}))) : List<&2, M.CmBlock>}, h)
                        case Con{+y5, +r5}:
                          match r5:
                            case Nil{}:
                              h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Nil{}}}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Nil{}}}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Nil{}}}}}}}))) : List<&2, M.CmBlock>}, h)
                            case Con{+y6, +r6}:
                              match r6:
                                case Nil{}:
                                  h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Nil{}}}}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Nil{}}}}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Nil{}}}}}}}}))) : List<&2, M.CmBlock>}, h)
                                case Con{+y7, +r7}:
                                  match r7:
                                    case Nil{}:
                                      h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Nil{}}}}}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Nil{}}}}}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Nil{}}}}}}}}}))) : List<&2, M.CmBlock>}, h)
                                    case Con{+y8, +r8}:
                                      match r8:
                                        case Nil{}:
                                          h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Nil{}}}}}}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Nil{}}}}}}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Nil{}}}}}}}}}}))) : List<&2, M.CmBlock>}, h)
                                        case Con{+y9, +r9}:
                                          match r9:
                                            case Nil{}:
                                              h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Nil{}}}}}}}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Nil{}}}}}}}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Nil{}}}}}}}}}}}))) : List<&2, M.CmBlock>}, h)
                                            case Con{+y10, +r10}:
                                              match r10:
                                                case Nil{}:
                                                  h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Nil{}}}}}}}}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Nil{}}}}}}}}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Nil{}}}}}}}}}}}}))) : List<&2, M.CmBlock>}, h)
                                                case Con{+y11, +r11}:
                                                  match r11:
                                                    case Nil{}:
                                                      h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Nil{}}}}}}}}}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Nil{}}}}}}}}}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Nil{}}}}}}}}}}}}}))) : List<&2, M.CmBlock>}, h)
                                                    case Con{+y12, +r12}:
                                                      match r12:
                                                        case Nil{}:
                                                          h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Con{y12, Nil{}}}}}}}}}}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Con{y12, Nil{}}}}}}}}}}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Con{y12, Nil{}}}}}}}}}}}}}}))) : List<&2, M.CmBlock>}, h)
                                                        case Con{+y13, +r13}:
                                                          match r13:
                                                            case Nil{}:
                                                              h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Con{y12, Con{y13, Nil{}}}}}}}}}}}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Con{y12, Con{y13, Nil{}}}}}}}}}}}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Con{y12, Con{y13, Nil{}}}}}}}}}}}}}}}))) : List<&2, M.CmBlock>}, h)
                                                            case Con{+y14, +r14}:
                                                              match r14:
                                                                case Nil{}:
                                                                  h => bo.absurd({Con{sp.hd(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Con{y12, Con{y13, Con{y14, Nil{}}}}}}}}}}}}}}}})))), sp.tl(M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Con{y12, Con{y13, Con{y14, Nil{}}}}}}}}}}}}}}}}))))} == M.cm.split.blocks(M.cm.split(B.mask(Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Con{y11, Con{y12, Con{y13, Con{y14, Nil{}}}}}}}}}}}}}}}}))) : List<&2, M.CmBlock>}, h)
                                                                case Con{+y15, +t}:
                                                                  h => %Equal.sym(List<&2, M.CmBlock>, M.cm.split.blocks(M.cm.split.cons(M.cm.block16(B.byte(y0), B.byte(y1), B.byte(y2), B.byte(y3), B.byte(y4), B.byte(y5), B.byte(y6), B.byte(y7), B.byte(y8), B.byte(y9), B.byte(y10), B.byte(y11), B.byte(y12), B.byte(y13), B.byte(y14), B.byte(y15)), M.cm.split(B.mask(t)))), Con{M.cm.block16(B.byte(y0), B.byte(y1), B.byte(y2), B.byte(y3), B.byte(y4), B.byte(y5), B.byte(y6), B.byte(y7), B.byte(y8), B.byte(y9), B.byte(y10), B.byte(y11), B.byte(y12), B.byte(y13), B.byte(y14), B.byte(y15)), M.cm.split.blocks(M.cm.split(B.mask(t)))}, sp.cons_blocks(M.cm.block16(B.byte(y0), B.byte(y1), B.byte(y2), B.byte(y3), B.byte(y4), B.byte(y5), B.byte(y6), B.byte(y7), B.byte(y8), B.byte(y9), B.byte(y10), B.byte(y11), B.byte(y12), B.byte(y13), B.byte(y14), B.byte(y15)), M.cm.split(B.mask(t)))) : {Con{sp.hd(_), sp.tl(_)} == _ : List<&2, M.CmBlock>}
                                                                    {==}

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  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=byte
  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=mask
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=bo.absurd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.cons_blocks
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.hd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.tl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=CmBlock
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.block16
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.split
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.split.blocks
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.split.cons