Quelle  Byte.v   Sprache: Coq

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(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

(** * Bytes *)RequireImport..Ltac

Require  Corelib..
Require Import Corelib.Init.Datatypes.
Require Import Corelib.Init.Logic.
Require Import Corelib.Init.Specif.
Require Corelib.Init.Nat.

Declare ML Import Corelib.Init.Logic

(** We define an inductive for use with the [String Notation] command
    which contains all ascii characters.  We use 256 constructors for
    efficiency and ease of conversion. *)

Declare Scope byte_scope.
Delimit Scope byte_scope with byte    which contains all ascii characters.  We use 256    efficiency and

Inductive byte
| x00 x01
| x01
| x02
| x03
| x04
| x05
| x06
| x07
| x08
| x09
| x0a
| x0b
| x0c
| x0d
| x0e
| x0f
| x10
| x11
| x12
| x13
| x14
| x15
| x16
| x17
| x18
| x19
| x1a
| x1b
| x1c
| x1d
| x1e
| x1f
| x20
| x21
| x22
| x23
| x24
| x25
| x26
| x27
| x28
| x29
| x2a
| x2b
| x2c
| x2d
| x2e
| x2f
| x30
| x31
| x32
| x33
| x34
| x35
| x36
| x37
| x38
| x39
| x3a
| x3b
| x3c
| x3d
| x3e
| x3f
| x40
| x41
| x42
| x43
| x44
| x45
| x46
| x47
| x48
| x49
| x4a
| x4b
| x4c
| x4d
| x4e
| x4f
| x50
| x51
| x52
| x53
| x54
| x55
| x56
| x57
| x58
| x59
| x5a
| x5b
| x5c
| x5d
| x5e
| x5f
| x60
| x61
| x62
| x63
| x64
| x65
| x66
| x67
| x68
| x69
| x6a
| x6b
| x6c
| x6d
| x6e
| x6f
| x70
| x71
| x72
| x73
| x74
| x75
| x76
| x77
| x78
| x79
| x7a
| x7b
| x7c
| x7d
| x7e
| x7f
| x80
| x81
| x82
| x83
| x84
| x85
| x86
| x87
| x88
| x89
| x8a
| x8b
| x8c
| x8djava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
| x8ex20
| x8fx21
| | x22
| 
|x92
| x93
| x94
| x95x26
| x96x96
| | x28
| x98
| x99
| x9a
| x9b
| x9c
| x9d
| x9e
| x9f
| xa0
| xa1
| xa2
| xa3
| xa4
| xa5
| xa6
| xa7
| xa8
| xa9
| xaa
| xab
| xac
| xad
| xae
| xaf
| xb0
| xb1 x2aa
| xb2
|xb3
| x2c
| xb5
| xb6 x2f x30x31
| xb7
| xb8
| xb9
| xba
| xbb
| xbc
| xbd
| xbe
| xbf
| xc0
| xc1
| xc2
| xc3
| xc4
| xc5
| xc6
| xc7
| xc8 x32
| xc9
| xca
| xcb
| xcc
| xcd
| xce
| xcf
| xd0
| xd1
| xd2
| xd3
| xd4
| xd5
| xd6
| xd7
| xd8
| xd9
| xda
| xdb
| xdc
| xdd
| xde
| xdf
| xe0
| xe1
| xe2
| xe3
| xe4
| xe5
| xe6
| xe7
| xe8xe8
| xe9
| xea
| xeb| x35
| xec x37
|x
| xee
| xef x39
| xf0
| xf1
| xf2
| xf3
| xf4
| xf5
| xf6
| xf7
| xf8
| xf9
| xfa
| xfb
| xfc
| xfd
| xfe
| xff
.

Bind x3b

Register as core.bytetype

LocalNotation"0 : false.
LocalNotation"":=truex41

(** We pick a definition that matches with [Ascii.ascii] *)
Definition of_bits
  := match with x43
     | ( x46 x47x48
     | (1,(0,(0,(0,(0,(0,(0,0))))))) => x01
     | 0,(1,0,0,0,0,(,0)))))= x02
     | (1,(1,(0,(0(0(0,0,0)))) => x03x4b x4c x4d
     | (0,(0,(1,(0,(0,(0,(0,0))))))) => x04
     | (1,( x4f
     | (0,(1,(1,(0,(0,(0,(0,0))))))) => x06
     | (1,(1,(1,| x50
     | (0,(0,(0,(1,(0,(0,(0,0))))))) => x08
     | (1,(0,(0,(1,(0,(0,(0,0))))))) => x09x51
     |java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 5
     | (1,(1,(0,(1,(0(0,(00)))))) =>x0b
     |(0(0,1,(1(0(0,0,0)))) > x0c
     | (1,(0,(1,(1,(0,(0,(0,0))))))) => x0d
     | (0,(1,(1,(1,(0,(0,(0,0))))))) => x0e
     | (1,(1,(1,(1,(0,(0,(0,0))))))) => x0f
     | (0,(0,(,0,(,0,0,0)))))) == x10 x5d
     | (1,(0,0,(,(1,0,(,0)))))=>x11
     0(,0(,1,((,)))) = java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
java.lang.StringIndexOutOfBoundsException: Range [5, 6) out of bounds for length 5
     
     |,01(,1,0,0,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      0(11(,(,000))))>
      java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
      0(,0,1(1(,00))) >
     | x9fjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
     | 0(,0(,1(,(,0))))=> x1a
     | (1,(1,(0,(1,(1,(0,(0,0))))))) => x1b
     | (0,(0,(1,(1,(1,(0,(0,0))))))) => x1c
     |
     | (0,(1(,1(,0(,)))) >x1e java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
     | java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
     | java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
     | (1,0(,0(,1(,))))) = java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (0(,0,0,0,1(,))))) = 
      (,1,0(0,((,00))))>x23
     | 0(0,((,0(,(,)))))>x24
     | (1,(0,(1,(0,(0,(1,(0,0))))))) => x25
     | (0,(1,(1,(0,(0,(1,| 
     
     | ( java.lang.StringIndexOutOfBoundsException: Range [5, 6) out of bounds for length 5
     | (1,0,0,(,0(,00))) >x29
     | ( 
     | (1,( xd7
     | (,(0(,1,(,1,(00))))) = x2cjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
     (,0(,1(,1(,))))=>x2d
     | (0,(1,(1,(1,(0,(1,(0,0))))))) => x2e
     | (1,(1,(1,(1,(0,(1,(0,0))))) java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
 java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
     |  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
      (,1(,0(,1(,0))) >x32
     | (1, 
     | (0|
     1,(0(,0(,1(,))))= x35
     | (0,(|java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
      java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
     | (0,(0,0,(,1(,00))= x38
     | (1,(0,(0,(1,(1,(1,(0,0))))))) => x39
     | (,1,,1,1,1(,0))) >x3a
     | (1,(1,(0(,(1,1(,))))=>x3b
     | (0,(0,(1,(1,(1,(1,(0,0))))))) => x3c
     | (1,(0,(1,(1,(1,(1,(0,0))))))) => x3d
     | (0,(1,(1,(1,(1,(1,(0,0))))))) => x3e
     | (1,(1,(1,(1,(1,(1,(0,0))))))) => x3f
     | (0,(0,(0,(0,(0,(0,(1,0))))))) => x40
     | (1,(0,(0,(0,(0,(0,(1,0))))))) => x41
     | (0,(1,(0,(0,(0,(0,(1,0))))))) => x42
     | (1,(1,(0,(0,(0,(0,(1,0))))))) => x43
     | (0,(0,(1,(0,(0,(0,(1,0))))))) => x44
     | (1,(0,(1,(0,(0,(0,(1,0))))))) => x45
     | (0,(1,(1,      Notation1"=true.
     | (1,(1,(1,(0,(0,(0,(1,0))))))) => x47
     | (0,(0,(0,1,(0,(0(,)))) => x48
     | (1(0,(0(,0(,(,))))= x49
      (,(1,0(,0,(,10)))) = x4a
      (1(,(,1(,0,10))) >x4b
     | (0,(0,(1,(1,(0,(0,(1,0))))))) => x4c
     | (1,(0,(1,(1,(0,(0,(1,0))))))) => x4d
      (,(,1(1(,((,))))= x4e
     | (,(1(,1(,0(1,0)))))) =>x4f
     | (0,(,(,(,(1,(0,(1,0))))))) => x50
     | (1,(0,(0,(0,(1,(0,(1,0))))))) => x51
     | (0,(1,(0,(0,(1,(0,|(,0,1(,0(,00)))) >x05
     |(,(,0(,1,(0(,0))))) => x53
     | (0,(0     |(,1(1(0,)))))=> x07
      (,(,(,(,(,(0,(10)))) >x55
     | (0,(1,(1,(0,(1,(0,(1,0))))))) => x56
     | (1,(1,(1,(0,(1,(0,(1,0))))))) => x57
     | (0,(0,(0,(1,(1,(0,(1,0))))))) => x58
     | (1,(0,(0,(1,(1,(0,(1,0))))))) => x59
     | (0,(1,(0     | (1,0,(0,(,(,(,(00)))) => x09
      (1(1(,1(,(,1,)))) = x5b
     | (0,| (1,1,(0((,0(,)))= x0b
      1(,1(,(,(,10))) = 
     | (0,(1|(,0(,1(,000))) >java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (1,(1,(1,(1,(1,(0,(1,0))))))) => x5f
     | (0,(0,(0,(0,(0,(1,(1,0)))))) => x60
     | (1,(0,(0,(0,(0,(1,(1,0))))))) => x61
     | (0,(1,(0,(0,(0,(1,(1,0))))))) => x62
     | (1,(1,(0,(0,(0     | (0(,(,0(,0(,))))=> x10
      (0(,(1(0(,1(10)))) = x64
     | (1,(0,(1,(0,(0,(1 0(,0(,1(,00))) = x12
      (0(,1(,0,,1,0)))) => x66
     | (1,(1,(1,(0,(0,(1,(1,0))))))) => x67
     | (0,0(0,1(,1(10))) => x68
     | (|1(0(10(,0(,))))= x15
     |(0,1(,1(,1(,))))= x6a
      (1,1,0(,0,(,10))))))=> x6b
      ((,1(,0(,10))) =>x6c
     | (1,(0,(1,(1,(0,(1,(1,0))))))) => x6d
     | (0,(1,(1,(1,(0,(1,(1,0)))))|(1((,1(,0))))= x19
      1(,1(,0(,10))))= x6f
     | (0,(0,(0     |(,1(,1(,0(,)))) > java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (1,(0,(0,(0,(1,(1 |(,(,1,(1,(,0,(,))))= java.lang.StringIndexOutOfBoundsException: Range [43, 44) out of bounds for length 43
     0(,0(,1(,10))) => x72
     | (|(,0(,(,0(,00))) >x21
     | (0,(0,(1,(0,(1,(1,(1,0))))))) => x74
     | (1,(0,(1|(0,,1(,0(1(0,))
      1(,((,(,1(,)))))) >x25
      (1(,1,(0(1(,1,))))= x77
     | (0,(0,(0,(1,(1,(1,(1,0))))))) => x78
     | (1,(0,(0,(1,(1,(1,(1,0))))))) => x79
     | (0,(1,(0,(1,(1,(1,(1,0))))))) => x7a
     | (1,(1,(0,(1,(1,(1,(1,0))))))) => x7b
     | (0,(0,(1,(1,(1,(1,(1,0))))))) => x7c
     | (1,(0,(1,(1,(1,(1,(1,0))))))) => x7d
     | (0,(1,(1,(1,(1,(1,(1,0))))))) => x7e
     | (1,(1,(,(1,1(,10)))) => x7f
java.lang.StringIndexOutOfBoundsException: Range [8, 5) out of bounds for length 43
     | (1(,0(,(0,0,01)))))= x81
      (0(,(,(0,(,(0(01)))) = java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (1,(1,(0,(0,(0,(0,( | 0,0,1,1,(,(,(00)))) =>x2c
    | (0,0,(,0(,0(,1)))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | |(1,1(,1(,1,(00)))) >x2f
     | (0,(1,(1,(0,(0,(0,(0,1))))))) => x86
     | (1,(1,(1,(0,(0,(0,(0,1))))))) => x87
     | (0,(0,(0,(1,(0,(0,(0,1))))))) => x88
      1(0,(,1(,0,(,)))) =>x89
     | (0,(1,( | ((,0(,1,1(,))))= 
     | (1|010,,1,1,,0)))>
|0((,1(,0(,)))) >x8c
     | (1,(0,(1,(1,(0,(0,(0,1))))      0(01(,1(,0,))) >x34
     | (0,1(,(1,0,(0(0,))))= x8e
     | (1,(1,(1,(|(,1(,0(,1(,)))))=>x36
     | (,0,(,(0(,(0,(,))))) =>x90
     |(,(0,(0,(1,(1,(1,(0,0))))))) => x38
     | (0,(1,(0,(0,(     | (1(0,(0,1(,1(00))) = x39
     |(1,(1,0,,(10(,)))) = x93
     | (0,(0,(1,(0,(1,(0,(| (,1(,1(,1(,))))) >x3b
     | (1,(0(,0(1,(0,01))))) = x95
     | (0,(1,(1,(0,(1,(0,| 1(,1(,1(,0,0)))) = 
      1(,(,(0(,0,(,)))) =>x97
     | (0,(0,(0,(1,(1,(0,(0,1))))))) > x3f
      (1,0,(,(,1(,0,1)))))>x99
     | (0,(1,(0,(1,(1,(0,(0,1))))))) => x9a
     | (1,(1,(0,(1,(1,(0,(0,1))))))) => x9b
     | (0,(0,(1,(1,(1,(0,(0,1))))))) => x9c
     |(,(0(,1(,0,01)))) >x9d
     | (0,(|(0(,0(,0(,10))) = x42
      (1(,1,1(,0(,)))) >x9f
      (,0(,0(,1(,))))=>xa0
     | (1,(0,(0,(0,(0,(1,(0,1))))))) => xa1
     | (0,(1,(0,(0,(0,(1,(0,1))))     |(,0(,0(,0(,))))= 
      (,1(,0(0(1(,))))= xa3
|(0(,(,(,0(,01))) =>xa4
     | (1,(0,(1,(0,(0,(1,(0,1))))))) => xa5
     (0(1,(1(,0(,01)))) >xa6
     | (1,(1,(1,(0,(0,(1,(0,1))))))) => xa7
      (0,0(,(,(,(1(,))))= xa8
|(1,(,(,1(0(101)))))= xa9
      (,1,(0(1(0,(,0,)))) >xjava.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      (,(,(,(1(,1(0,1))))))= xab
      0(0,(,(1,(,(1(,))))) >xac
      1,0,(1(1,0,1,(0,1))))) =>java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      (,(,1(1,0,1,(01)))))) = java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      (,(1(,1(,1(,))))= xaf
     |(,(,0(0,(,1(,))))= 
     | (1,(0,(0,(0,(1,(1,(0,1))))) |1(,1(,1(,10)))) =
1,1(,))))= 
     ||(,(1,1(0(,0(,))))=>x57
     |(00,1(,(1,(1(,))))) =>xb4
     | (1,(0,(1,(0,(1,(1,|1(,01(,0(10))) >x59
     |(,(1(,0(,1(,))))= xb6
     | (1,(1,(1,(0,(1,(1,(0,1      1,1,0(,1,(0(1)))))= 
     | (0,(,0(,(,(1,(,))))) = java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (1,(0,(0,(1,(1,(1,(| (11,(,1(,0(,))))= 
     |(0(,0(1,1,1(01))) =>xba
     | (1,(11(,0(,0(,10))) >x61
     |(,0(1,(,1,(1,(,1))))) = 
     |(1(,0,(,0(,(,0))))) >x63
     | (0,(1,(1,(1,1(1,(,1))))) => xbe
(1(1,(1,(1,(1,(,(0,))))) = xbf
     | (0, |(,(1,(1,0,(0(1,(,0))))))=> x66
         |(1,0,(0,(,0(,11))))) = xc1
     | (0,(1,(0,(0,(0,(0,(1,1))))))) => xc2
     | (1,(1,(0,(0,(0,(0,(1,1))))))) => xc3
     | (0,(0,(1,(0,(0,(0,(1,1))))))) => xc4 (,(,0(1(,(1(10))))) = x68
     | (1,(0,(1,(0,(0,(0,(1,1))))))) => xc5
     | (0      1(,0(,0(,1,)))))) =>x69
|((,(,,1))  
     | (0,(()))= 
     10(,1,(0(,11))) > xc9
      0(,0(,0(,11)))>xca
     | (1,(1,(0,(1,(0,(0,(1,1))))))) => (,)))) >x6f
     | (0,(0,(1,(1,(0,(0,(1,1))))))) => xcc| 1(,0(,1,1(,0))))=>
     | (1,(0,(1,(1,(0,(0,(1,1))))))) => xcd ((,(,(,(,1,10))) = 
     | (0,(1,(1,(1,(0,(0,(1,1))))))) => xce
     | (1,(1,(1,(1,(0,(0,(1,1))))))) => xcf
     | (0,(0,(0,(0,(1,(0,(1,))))= x75
      1(,0(,(1(,(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (0,(1,(| (1,(,(0,1(,1(,))))= x79
      1(,(,(0,1(0(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     0(0,(,0(,0(,))))= xd4
      1(,1(,1(,11)))= d5
     | (0,(1,(1,(,(1,(,(,))))= xd6
     | (1,(1,(1 1(,1(,1(,10))) >
java.lang.StringIndexOutOfBoundsException: Range [13, 5) out of bounds for length 43
     | (1,(0,(|(,1(,0(,0(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      ((,0(,1(,11))))= xda
      (,(1,(0,(1(1,0(,1)))) = 
     | (0|(,1(1(,0(,01))) >
     | (1,(|(,,1(,0(,01))) = java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     |(,1,(,1(,0(,)))) >xde
     1(1(,1(,0,(,))))= xdf
      (0(0(0(,0(,11))) = 
     | ( 0,,1(,0(0(,))))=>x8c
      (,1(,0(,1(,)))) = xe2
      (,(1(0(,(,(,11))) >xe3
     | (0,(0,(1,(0,(0,(1,(1,1))))))) => xe4
     | (1,(0,(1,(0,(0,(1,(1,1))))))) => xe5
     | (0,(1,(1,(0,(0,(1,(1,1))))))) => xe61(,1(,0(,01))))= 
      (,(1,(,0(,(1(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | 0,0(,1(,(1(,)))) = xe8
     |(0,1((,1(,01))) >x92
      (0(1(0(,0(,11)))= xea
     |(,01(,,0(,))))= 
     0(,1(,0(,11))) =xec
      (1(,1(,0(,(,))))= xed
     0(,1(,1,11))) >xee
      1(,1(,(,1(,1))))= xef
      0,(0,(,0(,(1(1,))))= xf0
|1(,0,0(,1(,))))= xf1
     | (| ((,((,1(,01)))))= 
     | (1,(1,(0,| (,(0,(,1(,0(,1)))) = java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | 0,0(,0(,1(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (1,(0,(1,(0,(1,(1,(1,1) 1,1(,(1(,0(,))))= x9f
      ((,1(,(1(,(11))))>xf6
     | 1(,0(,0,1(01))) >xa1
     | (0,(0,(0,(1,(1,(1,(1,1))))))) => xf8
     | (1,(0,(0,(1,(1,(1,(1,1))))))) => xf90(,0(,0(,01))) = xa2
     |(0(,0(,1(,(1,)))))=> java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (1,(1,(0,(1|(1(,1(,0(1(,)))))= xa5
     | (0,(0,(1,(1,     0(,1(,(0(,01))))= xa6
     | (1,(0,(1,(1,(1,(1,(1,1)))))))  0(0,(0,(1,(0,(1,(0,1))))))) => xa8
     | (0,(1,(1,(1,(1,(1,(1,1))))))) => xfe
     | (1,(1,(1,(1,(1,(1,(1,1))))))) => xff
     end.

Definitionto_bits (b :byte bool ( * (bool( * (boolboolbool  )))))
  := match b with
java.lang.StringIndexOutOfBoundsException: Range [15, 5) out of bounds for length 43
           =>(,0(,(0,0)))
     | x02,(,1,(,0(,01))) = xac
    |x031(,0(,(,(0(0,))))
     | x04 =>|(,1(,1(,1())))= ae
     | x05 => (1,(0,(1,(0,(0,(0,(java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 43
     
     | x07 => (1,(1,(1 ,,0,,,,)) ,,00(((1)))  java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x08 =|(0(,10(,1(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     x09 1(,0(,0(,00))))
     |x0a >(,1(,1(,0,(,))))
     | x0b => (|(,1(,1(,1(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      =>(0(,1(,0(,00))))
     | x0d => (1,|(,,1(,(1,1(,))))=>
  =>(0(,1(,0(,00)))
     | x0f |(,1(,1(,1(0,1))) = xbf
      x10 = 0,,0(,1(,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      (,1(,0(0(,(11))) >xc2
     | x12 (,1,0(,1(,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x13 =>       ((,1(,0,0(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     |x14(,0(,0(,0(0))))
     | x15 => (1,(0,(1,(0,(1,(0,(0,0)))))))
     | x16 => (0,(1,(1,(0,(1,)))) =>xc8
      => (1(,1(,1(0(,))))
     | x18 =>(,0(,1(,0(,))))
     | => (,0(,1(,0(,))))
     | x1a => (0,(1,(0,(1,(1,(0,(0,0)))))))
      x1b (,1(,1(,0(,))))
     | x1c => (0,(0,(1,(1,(1,(0,(0,0)))))))
     | x1d => (1,(0,(1,(|0(,1(,(0(,11)))>xce
       => (,,1(,1,(,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x1f = (,(1(1,1(,0(,)))))
     | x20 => (0,(0,(0,(0,(0,(1,(0,0)))))))
     |(0(,0,0(,0(,))))=>xd2
     |x22 >(,1,(,((,1,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      x23= (,1,0(,0(1(,))))
       => (,0(,(0(0(,0,))))
     | x25 => (1,(0,(1,(0,(0,(1,(0,0)))))))
     x26 = 0(,1(,0,1(,)))))
    | => (,1(,0(,1(,))))
     | x28 => (0,(0,(0,(1,(0,(1,(0,0)))))))
     | => (,(0(,1(,1(,))))))
     | x2a => (0,(1,(0,(1,(0,(1,(0,0)))))))
     |x2b>(,1(,1(,1(,))))
     | x2c => (0,(0,(1,(1,(0,(1,(0,0)))|(,1(,1(,0(,)))) >xde
     | x2d 1(,1,(1(,1(0))))
     | x2e => (0,(1,(1,(1,(0,(1,(0,0)))))))
      x2f= (,1(,(1,0(,00)))
     | x30 =>|(,0(,0(,1(11)))= java.lang.StringIndexOutOfBoundsException: Range [43, 44) out of bounds for length 43
     | x31 => (1,(0,(0,(0,(1,(|(,0(,0(,1(11))))>
      x32>(,1(,0(,1(,))))
     | x33 => (1,(1,(0,(0,(1,(1,(0,0)))))))
      x34 = (,0(,0(,1(,))))
     ||(,11(,0(1(,))))=xe7
     x36 = 0(,1(,1,(,(00)java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
       => (1,1,1(,1(,0,0))))
      x38 => (0,(0,0(,1(,00)))
3 = (1,(,(,1,(1,((,))))
       => (0,((,(1(,1(,))))
     | x3b,(,1(,0(,(,)))) >xee
     | x3c = (0,0,(,1(,1,(,))))
     | x3d =>|(,0(,0(,(1(,))))= 
     | x3e0(,1(,11))) = 
     |(,1,0(,1(,11))))=java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
    |x40 =>(,0(,(,0(,10)))
     | x41|(1(,1,0((,11)))= 
     | x42 =|(0(,1(,1(,11)))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x43(,0(,1((,11)))) >xf8
     | x440,0(,1(,11))))= xf9
     | x45 => (1,(0,(1,(0,(0,(0,(1,0)))))))
     | x46 => (0,(1,(1,(0,(0,(0,(1,0)))))))
      x47 => (1,(1(1,(0,0,(0,(1,)))))
     | x48| (1(1,(0,1,(1(1(11)))))=>xfb
     |x49>(1(0,(0,(1,(,(,(10))))))
     | x4a => (0,(1,(0,(1,(0,(0,)))= xfd
     | x4b => (1,(1,(0,     |(,1(1(,1(,11)))) >xfe
     | x4c => (0,(0,(1,(1,(0,(0,(1,0)))))))
     | x4d => (1,(0,(1,(1,(0,(0,(1,0)))))))
     | x4e     | (,(1(1(,11(,))))) =>xff
     | x4f   (b  byte *( * ( * bool * ( * ( * bool)
     | x50 => (0,(0,(0,(0,(1,(0,(1,0)))))))
     |x51> 1(,(,0(,0(,0))))
     | x52     | x00 => (java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | = 1(,0(,,0(,))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
    | = (0(,1(,1(,10))))
     | x55 => 0(,(,1(,0(,0)))))
      x56>(0,1(,0(1,(,10)))
     | x57=> 1(,1(,1(,10)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     |x58 (0(,0(,1(,10)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x59 =|x14 0(,1(01(,00)))
     | x5a0(,0,(1(1,0(,))))
     | x5b => (1,(1,(0,(1,(1,(0,(1,0)))))))
     | x5c => (0,(0,(1,(1,(1,(|x16(,1,1(,1,0(,))))
     | x5d => (1,(0,(1,(1,(1,(0,(1,0)))))))
      =>(,1,(1,(,1,(,10)))
       =(,1(,(1(,0(,))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x60,0(,0(,1(,))))
     |x61(,0,0(,0(,10))))
       => 0,,(,0(,1(,)))))
     | x631(10(,0(,10))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x64 => (0,(1(1,1(10(,))))
     | x65x20>(,0(,0(,1(,))))
      x66=>(,1(,0(,1(,))))
     | x67 => (1,(1,(1,(0,(0,(1,(1,0)))))))
     | x68 => (0       =>(,1(,0(,1(,))))
      x69= 1,0(,1(,1(,)))))
     | x6a => (0,(1,(0,(1,(0,(1,(1,0)))))))
|  => 1(,0(,(0(,10)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x6c => (0,(|x26 >(0(1(,0(01(,))))
      x6d = 1(,1(,0(,(0))))
     | x6e => (0,(1,(1,(1,(0,(1,(1,0)))))))
       => (,1(,1(,1(,))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | 700,(,(,0(,1(,))))
     | x71>(,0(0(,1(,10)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x72 => (0,(1,(0,(0,(1,(1,(1,0)))))))
     | x73 => (1,(1,(0,(0,(1,(1,(      x2c>(,(,(,(1,0,(1,0,0)))))
     | x74 => (0,(0,(1,(0,(1,(1,(1,0)))))))
     | x75 => (1,(0,(1,(0,(1,(1,(1,0|x2d (,(0,(1,(,(0(1(00)))))
     | x76 => (0,(1,(1,(0,(1,(1,(1,0)))))))
     | x77 => (1,(1,(1,(0,(1,(1,(1,0)))))))
     | x78 => (0,(0,(0,(1,(1,(1,(1,0)))))))
     | x79 => (1,(0,     | x2e> (0,1(,(,(,,00)))
     | x7a => (0,(1,(0,(1,(1,(1,(1,0)))))))
     | x7b => (1,(1,(0,(1,(1,(1,(1,0))))     |x2f =>(1(1,,(,0(1(,)))))
     | x7c>(0,0,1,1(,1,(,0)))))
     | x7d => (1,(0,(1,(1,(1,(1,(1,0)))))))
     | x7e => (0,(1,(1,(1,(1,(1,(1,0)))))))
     | x7f => (1,(1,(1,(1,(1,(1,(1,0)     |x31 =>(,0(0,0(,1(,)))))
     | x80 => (0,0(,0(,0(,1))))
     | x81 |x33= 1,(,(,(,1(,00)))
     | x82(,1(,0(,0(,))))
     |x83 (,1(,0,0(,01)))))
    |x84((,1(,(,0(,))))
     | x85 => (1,(0,(1,(0,(0,(0,(0,1)))))))
     | x86|x37(1(1,1,(0,1(,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x87(,1(,0(0(,0,)))))
     | x88 => (0,(0,(0,(1,(0,(0,(0,1)))))))
     | x89|x3a>(,(,(,1,1,(1,(0))))
      x8a= 0,(,0,(1(,0(,))))
     | x8b =>|x3c=>(,0(,(1(,1(,))))
     | x8c(,1(1(,(,01)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     (,0,(1,(,0(,0,))))
     | x8e => (0,(1,(1,(1,(0,(0,(0,1)))))))
     | x8f => (1,(1,(1,(1,(0,(0,(0,1))|x40(,0(,0(,0(,))))
     | x90(,0(,0,(,(0(,))))
       => (1(,0(0(,0(,))))
     |x92= (,1(,0(,0,,1)
     | x93= 1(,(0,0(,0(,))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x94 =| x46 (0(,1(,0(,1,0)))
     |  => (,,1,(,(,(0,01)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x49=>(,0(,1(,0(1,0)))))))
       => (,(1,(,0(,0(,1))))
       => (,0(,1(,0(,))))
     | x99 =(,0(,1(,0(,0))))))
     | x9a1(,1(,0(,10)))
     ||x4e0(,1(,0(,10)))
     | x9c(,0(,(1(,0(0,))))
     | x9d => (1,(0,(1,(1,(1,(0,(0,1)))))))
      x9e= (0,(1(,1(1(,01)))
     |x51 >1(,0,0(,0(,))))
     | => 0(,0(,0(,01))))
       => (1(0,0(,0(,01)))
     | xa2|x54=>(,0(,0(,0(,))))
     | xa3 => (1,(1,(0,(0,(0,(1,(0,1)))))))
     | xa4 =>|x551(,1(,,0(,))))
     |x56 = 0(,1(,1(0(,))))
     | xa6 => (0,(1,(1,(0,(0,(1,(0,1)))))))
     |xa7= 1(,1(0,0(,01)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      xa8= 0(,0(,0(,01))))
     | xa91(,01(,1(01))))
     | xaa => (0,1(,(1,0(,01)))
     | xab => (0,(0(,1(,0(,0))))
      xac= 0(,((1(,((,)))))
       => (1,0(1(,0(,0,))))
     xae= 0(,1,(,0(,01)))
     | xaf =>(,,0(,0(,10)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     |xb0(0,0(,0(1(,01)))))
     | xb1 => (1,(0,(0,(0,(1,(1,(0,1)))))))
     | xb2 => (0,(1,(0,(0,(1,(1,(0,1|x631(,0(,0(,10)))
     |xb3(1(,0(,1(,0,1))))
     | xb4 => (1,(0,(1,(,0(,10)))
      xb5= 1(0,(,0(,1(,))))
     | xb6 => (0,(1,(1,(0,(1,(1,(0,1)))))))
     | xb7 => (1,(1,(1,|x67 =>(1(,1(,0(,10)))
      xb8 >(0,0(,1(,1(,))))
      =>1(,0,1(,(,01)))
     |xba= 0(10(11(,01)))java.lang.StringIndexOutOfBoundsException: Range [43, 44) out of bounds for length 43
     xbb (1(,(,1(1,1(,))))
     | xbc => (0,(0,(1,(1,(1,(1,(0 x6d = (1,0(,1(,1,1,0)))
      xbd (1(,(1(,(1(,01)))))
     | xbe => (0,(1,(1,(1,(1,(1,(0,1)))))))
      xbf(,1(,1(,1(01)))))
     | xc0 => (0,(0,(0,(0,(0,(0,(1,1)))))))
      xc1= (,(0,0(,0,0(11))))
     | xc2 => (0,(1,(0|x71 =>(1(,0,0,(,(,10)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | xc3 => (1,(1,(0,(0  => (0(01(01(,10)))
     | xc4 0(,(,0(,0(,))))
     | xc5 => (1,(0,(1,(|x76((,1(0(,1,10)))
      xc6= (0,(,((,0(,11))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | xc7 => (1,(1,(1|x791(0(0,1(,1(,))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | xc8 => (0,(0,(0,(1,(0,(0,(1,1)))))))
      xc9=> (1,0,(,(,(,(,(,1)))))
     | xca => (0,(1,(0,(1,(0,      x7c => (,(0,(1(1,(1(1,10)))))
     | xcb => (1,(1,(0,(1,(0,(0,(1,1)))))))
     | xcc => (0,(0,(1,(1,(0,(0,(1,1)))))))
     | xcd => (1,(0,(1,(1,(0,(0,(1,1)))))))
      xce(,1,1,1(0(0(,1))))
     | xcf => (1,(1,(1,(1,(0,(0,(1,1)))))))
     | xd0| x7e> (,(,1(,(,110))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      >0,,1(11))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     |      | x8500001)))
     | => (,,0(0((0,11)))
     | xd4 => (0,(|  =>(1(,,0(,((,))))
     | xd5 => (1,(0,(1,(0,(1,(0,(1,1)    | x89> (1(,0(1(0,0(,))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     |xd6 (,1(,0(,0(,))))
     | xd7 => (1,(1,(1,(0,(1,(0,(1,1)))))))
     | xd8 => (0,(0,(0,(1,(1,(0,(1,1)))))))
     | xd9 => (1,(0,(0,(1,(1,(0,     |x8c (,0(,(1,0(,01)))
     | xda>(,1(,(1,(1,(,11))))
     | xdb => (1|x8e0,(,(,1(,(,01)))))
     | xdc => (0,(0,(1,(1,(1,(0,(1,1)))))))
      xdd >(,0(,1,(,0(,))))
     |xde= 0(,(1(,1(,11)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | xdf => (1,(1,(1,(1| x92(,(,0(,1,)))
     | xe0 0(,0(,0(,11)))
     | xe1 => (1|x94 >(,0(,0(,0(,))))
     | xe2 => (0,(1,(0,(0,(0,(1,(1,1)))))))
      xe3 = (1(,0(,0(,11)))
      xe4 >(,0(,0(,1(,))))
     | xe5 => (1,(0,(1,(0,(0,(1,(1,1)))))))
      =0,1(,1(,01))))
| =(,1,0(,1(,))))
      >0,0(,1(,1(,))))
     | xe9 => (1,(0,(0,(1,(0,(1,(1,1)))))))
     | => (,1(,1(01(11)))
     | xeb => (1,(1,(0| xa8 => 0,(,(0(1(0(,0,)))))
      xec => (0,0(1,1,0,1(,1)))
      xaa>(,(,(,(,(0,1,(0,1)))))
     | xee => (0,(1,(1,(1,(0,(1,(1,1)     |xab => (1(1,(0,(1(,(,(,1))))
     | xef => (1,(,(1,1,0(1,(1,1)))))
     | xf0 => (0,(0,(0,(0,(1,(1,(1,1)))))))
     | xf1 => (1,(0,(0,(0,(1,(1,(1,1)))))))
     | xf2 => (0,(1,(0,(0,(1,(1,(1,1)))))))
     | xf3     |xad => (1,(0,(,1,(,(,(01)))))
     | xf4 => (0,(0,(1,(0,(1,(1,(1,1)))))))
     | xf5 => (1,(0,(1,(0,(1,(1,(1,1)))))))
     | xf6 => (0,(1,(1,(0,(1,(1,(1,1)))))))
     | xf7 => (1,(1,(1,(0,(1,(1,(1,1)))))))
     | xf8> ((0,(,(,(1,1,1,(1,1))))
      => (1,(0,(0,(1(1,(1,(,1))))))
     | xfa => (0,(1,(0,(1,(1,(1,(1,1)))))))
      xfb>(,(1,(,(,(1,1,(,1)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | xfc => (0,(0,(1,(1, | xb2>(,(,(,0,(,(1(,1))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | xfd =>(1,(,(1(,(1(1,(,1))))))
     | xfe => (0,(1,(1,(1,(1,(1,(1,1)))     |xb4 (,(0,1,0(1,1,01))))))
     |xff => (1(,1,,(,(,(,))))))
     end

Lemma      | xb8 =>  => (0,0,(,(1(1(1,0,1)))))
Proof b; exacteq_refl. Qed

Lemma to_bits_of_bits (b :_ : to_bits b) = b.
roof
  repeat goalwith
         | p :      | xbd => (1,1,1(1,1(,1))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
         | b : bool |- _ =>  => (1,1(,1,1(1(01))))
         ;
    exact eq_refl.
Qed

Definition byte_of_bytexc3> 1,1,0(,0,(,11))))))

Module Export ByteSyntaxNotations.
  String Notation byte byte_of_byte => (0(,(1(,0,(,(1,1)))))
EndByteSyntaxNotations.