PROOF.sp.mod_tail: 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 408-475 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=408&end_line=475

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 list of whole blocks splits with no tail
def sp.mod_tail(ys: List<&2, U32>) -> {Nat.mod(B.len(ys), 16n) == 0n : Nat} -> {M.cm.split.tail(M.cm.split(B.mask(ys))) == Nil{} : List<&2, U32>}:
  match ys:
    case Nil{}:
      h => {==}
    case Con{+y0, +r0}:
      match r0:
        case Nil{}:
          h => sp.absurd_tail(0n, Con{y0, Nil{}}, h)
        case Con{+y1, +r1}:
          match r1:
            case Nil{}:
              h => sp.absurd_tail(1n, Con{y0, Con{y1, Nil{}}}, h)
            case Con{+y2, +r2}:
              match r2:
                case Nil{}:
                  h => sp.absurd_tail(2n, Con{y0, Con{y1, Con{y2, Nil{}}}}, h)
                case Con{+y3, +r3}:
                  match r3:
                    case Nil{}:
                      h => sp.absurd_tail(3n, Con{y0, Con{y1, Con{y2, Con{y3, Nil{}}}}}, h)
                    case Con{+y4, +r4}:
                      match r4:
                        case Nil{}:
                          h => sp.absurd_tail(4n, Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Nil{}}}}}}, h)
                        case Con{+y5, +r5}:
                          match r5:
                            case Nil{}:
                              h => sp.absurd_tail(5n, Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Nil{}}}}}}}, h)
                            case Con{+y6, +r6}:
                              match r6:
                                case Nil{}:
                                  h => sp.absurd_tail(6n, Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Nil{}}}}}}}}, h)
                                case Con{+y7, +r7}:
                                  match r7:
                                    case Nil{}:
                                      h => sp.absurd_tail(7n, Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Nil{}}}}}}}}}, h)
                                    case Con{+y8, +r8}:
                                      match r8:
                                        case Nil{}:
                                          h => sp.absurd_tail(8n, Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Nil{}}}}}}}}}}, h)
                                        case Con{+y9, +r9}:
                                          match r9:
                                            case Nil{}:
                                              h => sp.absurd_tail(9n, Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Nil{}}}}}}}}}}}, h)
                                            case Con{+y10, +r10}:
                                              match r10:
                                                case Nil{}:
                                                  h => sp.absurd_tail(10n, Con{y0, Con{y1, Con{y2, Con{y3, Con{y4, Con{y5, Con{y6, Con{y7, Con{y8, Con{y9, Con{y10, Nil{}}}}}}}}}}}}, h)
                                                case Con{+y11, +r11}:
                                                  match r11:
                                                    case Nil{}:
                                                      h => sp.absurd_tail(11n, 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{}}}}}}}}}}}}}, h)
                                                    case Con{+y12, +r12}:
                                                      match r12:
                                                        case Nil{}:
                                                          h => sp.absurd_tail(12n, 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{}}}}}}}}}}}}}}, h)
                                                        case Con{+y13, +r13}:
                                                          match r13:
                                                            case Nil{}:
                                                              h => sp.absurd_tail(13n, 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{}}}}}}}}}}}}}}}, h)
                                                            case Con{+y14, +r14}:
                                                              match r14:
                                                                case Nil{}:
                                                                  h => sp.absurd_tail(14n, 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{}}}}}}}}}}}}}}}}, h)
                                                                case Con{+y15, +t}:
                                                                  h => %Equal.sym(List<&2, U32>, M.cm.split.tail(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)))), M.cm.split.tail(M.cm.split(B.mask(t))), sp.cons_tail(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)))) : {_ == Nil{} : List<&2, U32>}
                                                                    sp.mod_tail(t)(Equal.trans(Nat, Nat.mod(B.len(t), 16n), Nat.mod(Nat.add(16n, B.len(t)), 16n), 0n, Equal.sym(Nat, Nat.mod(Nat.add(16n, B.len(t)), 16n), Nat.mod(B.len(t), 16n), sp.mod16(B.len(t))), h))

Uses (17):
  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=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  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=sp.absurd_tail
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.cons_tail
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/PROOF.bend&name=sp.mod16
  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.cons
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-cipher-modes@0.1.0.0/cipher_modes.bend&name=cm.split.tail