Quelle  Byte.v   Sprache: Coq

(************************************************************************)
(*         *      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 *)

Require  CorelibInit.
Require Import Corelib.Init.DatatypesRequire ImportCorelib.InitLtac
RequireInit.
Require Import Corelib
Require Corelib.Init.Nat.

Declare ML Module "rocq-runtime.plugins.number_string_notation".

(** 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

Inductive :=
| x00
|java.lang.StringIndexOutOfBoundsException: Range [5, 3) out of bounds for length 5
| 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
| x22x91
| 
| x24
| x25
| 
|  
java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
|
|x2
|
| 
|
| 
| 
|x
| 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
 xe8
|
|
|
|  ed
|
| java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
|
| byte..
| x3d
| x3e  "0=
| x3f
| x40  " := .
| java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
| x42  b 
|
| x44
| x45
|
|
| java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
| x49(,1(,,(,0))))>
| x4a,,,0(,)))
| 
|
| java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
| x4e
|java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
 java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
| 
| x52
| x53
| x54
| x55
| x56
| x57
| x58
| x59(,)))  
| ,,(,,0(,))))= 
| java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 43
| x5c0((,1(())) >
|x5d
| x5e((,01(,00))) x11
 |(,1(0,0,1,(,00))))) >x12
| 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
|     |(1(,(,0,(,,00))) >x15
| x8a
| x8b
| x8c
| x8d
| x8e
| x8f
| x90
| x91
| x92
| x93
| x94|(0(1(,0,1(,(,0)))) = x16
| x95
| x96
| x97
| x98
| x99
| x9a
| x9b
| x9c
| x9d
| x9e| (,0(,(,(,0(,))))= x18
| x9f
| xa0
| xa1
| xa2
| xa3
| xa4
| xa5
| xa6
| xa7
| xa8(,1(,1(,0(,0)))) =>java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
| xa9
| xaa
|xab
| xac0(,1(,1(,0,))))= 
|xad
| xae
| xaf
| xb0
| xb1
| xb2
| xb3
| xb4
| xb5
| xb6
| xb7
| xb8
| xb9
| xba
| xbb
| xbc
| xbd
| xbe
| xbf
| xc0
| xc1
| xc2
| xc3
| xc4
| xc51,(,0(,0(,00)))))=>x21
| xc6
| xc7
| xc8
| xc9
| xca
| xcb|(,1(,0(,(,00))))>x22
|   1(1(,0,(,1(,))))= x23
| xcd(,0,(,0(,1(,0)))) = java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
| xce
| xcf
| xd0
| xd1
| xd2
| xd3
| xd4
| xd51((0,1(,1(,))))= x29
| xd6
| xd7
| |0(,1(,0(,00))))) >
| xd9
| xda
| xdb
| xdc
| xdd
| xde
| xdf
|| ((,1(,0(,00)))) = java.lang.StringIndexOutOfBoundsException: Range [43, 44) out of bounds for length 43
|xe1
| xe2
| xe3
| xe4
| xe5
| xe6
| xe7
|xe8
| xe9
| xea
| xeb
| xec
| xed
| xee
| xef
| xf0
| xf1
| xf2
| xf3
| |(0(,0(,1(,0,)))))= x32
| xf5
|xf6
| xf7
||(,(01(,1(,00))) >x35
|xf9
| xfa
| xfb
| xfc
| xfd
| xfe
| xff
.

Bind Scope byte_scope with,,((,1(,))))) >x38

Register byte0(1,0(,1(,00))))= 

Local,1(1(,(00))) = java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
  " : true.

(** We pick a definition that matches with [Ascii.ascii] *)
Definition of_bits00(0,10))))= 
  := match,0(,1(,010))) >
     | (0,(0|(0(1(,1(,0(,))))>x4a
     | (|(,10(,0(,(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (0,|(,1(,10(,10))) >x4e
     | 1(,1(,0(,0))  
     | (0,(| ,0(,(java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      1(,,0(,0(,0)))) = x05
     | (0,(1,(1,(0 1,((00(,10)))= x53
      ((,,0,(0,(0,(0)) >x07
     | (0,(0, ((10(,)))= java.lang.StringIndexOutOfBoundsException: Range [43, 44) out of bounds for length 43
 ,(00(,)))>
     | (0,(1,(0,(1,|(,,0(,1(,10))) >x5b
     (1(,0(,0(,00)))) =x0b
     | (0,(0,|(,0(,1(,0(,))))=>x5d
      1(,((,0(,(,))))= x0d
     | (0,(1,(1,(1,(0,(0,(0,0))))))) => x0e
     | (1,(1,(1,(1,(0,>java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
    (,00(,1(,00))) >
     | (1,(0,(0,(0,(1,(0,(0,0))))))) => |(00(,00(,(,)))) > 
     |(,1(,0(,0(,))))=>
     | (1,(1,(0,(0,(1,(0,(0,|(,1(,0(,1(,0))))=> 
     | (0,(0,(1,(0|0(,0(,0(,1,))))=x68
     | (,(,1(,1(,(,0))) >x15
     | (0|(0(,0(,(0(,10))) >x6a
     | (1,(|(,1(,1(,((,))))) =>x6b
     | (0,(|(,0(,1,(,1(10))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      (1,0,0(,1(0,(0,0)))) >x19
     | (0,(1,(0,(1,(1,(0,|(,1(,1(,1(,)))) >x6f
     | 1(,0(,1(,00))))= x1b
     | (0,(0,(1,(1,(1,(0,(0,0))))))) => x1c
     | (1,(0,(1,(1,(1,(0,(0,0))))))) => x1d
     01(,(1,1(0,0,)))) >x1e
     | (1,(1,(1,(1,(1,(0,(0,0))))))) => x1f
     | (0,(0,(0,(0,(0,(1,(0,|(,1(00(,1(,))))=>x72
      1(,0,0(,1(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (0,(1,(0,(0,(0,(1,(0,0))))))) => x22
     | (1,(1,(0,(0,(0,(1,(0,0))))))) => x23
      0,0(,0(,(,(0,0))))) => x24
|(,0(,00(,00)))))= 
     | (0,(1,(1,(0,|(,1(,(,11(,)))) >x77
     | (1 1(,(1(,1(,)))>
     | (0,(0,(0,(0,(0,(0,(0,1))))))) => x80
     | |(10(,0(,0(,)))) >x81
     | (0|(,1(0(0,0(,0))) >x82
     | (1,(1,(0,(1,(0,(1,(0,0))))))) => x2b
    ((((,010,)))) = x2c
     | (1,(0,(1,(1,(0,(1,(0| (0(,1(,0(,01)))) >x84
     | (0,(1,(1,(1,(0,(1,(0,0))))))) => x2e
      (1(,1(,0((,)))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (0,(0,(0|(,0(,,0(,01)))= x89
     | (,0(,0(,(,00))) >x31
     | (,(1(0,0,(1(1(0,0))))) = x32
     | (1,(1,(0,(0,(1,     | (,(0,1(1,0(,01)))) = x8c
     | (,(0(,0(,1(,))))= x34
     | (1,(0,(1,(0,(1,(1,(0,0))))))) => x35(,1(,0(0(01))) >x8e
      0(,1(,1(,00))))=> 
     | (1,(1,(1,(0| ((,001(0,01)))= x90
 (0
 ,(,(,1(,,))))>
     | (0,(1,(0,(1,(1,(1,(0,0))))|1(1(,0(1(,01)))) =x93
     1(,0(,1(,00))))= 
     | (0,(0,(1,(1,(1,(1,(0,0))))))) => |1,1(,1(0(,))))= x95
      (,0(,1(,1(,0)))) >x3d
     | (0,(1,(1,(1|(,1(,0(((1))))= 
=
     | (0,(0,(0,(0,|(,(,0(,10(,1)))) = java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (1,(0,(0,(0,(0,(0,(1,0))))))) => x41 1(,((,1(,(,))))= 
      (0,1(,0(,0(,))))=>x42
     | (|(11(,1,1(,01))))= 
     | (0,(0,(1,(0,(|0(,0(,0(,01))) = java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     |1(,1(,0(,10))) >x45
     | (0,(1,(1,(0,(0,(|1,(,0(,0(1,01))) =xa3
      (00(,0(,1(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (|(0,1,(,0(,1(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (1,(0,(0,(1,(0,|((,0(((,01))) >
      (1,(,0(,(,1(,)))))))=>xa9
     | (| 0(,0(,0(1(,1))))= aa
     | (0,(0,(1,(1,(0,(0,(1,0))))))) => x4c
     | (1,(0,(1,(1,(0,|(1(,0(,0(,0,)))))>xab
     | (0|(,0,1(,0(,01))))= 
     | (1,(1,(| (,0(,1((,0,)))))> xad
     | (0,(0,(0,(0,(1,(0,(1,0))))))) => x50
     | (1,(0,(  01(,1((,01)))) >xae
     | (0,(1,(0,(0,(1,(0,(1,0))))))) => x52
     | (1,(1,( (1(,1(,0(,01))) >xaf
     | (0,(0,(1,(0      00(,0,1(,01))) >xb0
     | (,0(,0(,0(,)))))= x55
     | (0,(1,(1,(0,(1,,0,1))) >xb2
      (,(1,(,(0,1(0,10))) = x57
     | (0,(0,(0     |0(,10,01))) = 
     | (,(0(,(,1(,(,0))))= x59
     | (0,(1,(0,(1,(1,(0,(1,0))))))) =      0(1(,,1(,01))) >xb6
    |(,1(,1(,(0(10)))) >x5b
     | (0,00(,11(1(,))))>xb8
     | (1,(0,(1,(1,(1,(0,(1,0))))))) => x5d
     | (0,(1,(1,(1,(1,(0,(1,0))))))) => x5e
     |(1(,1(,1(,(10))) >x5f
     | (0,(0,(0,(0, (01(,1(,,(0)))) = xba
     |(1,0(,0(,1(,))))= x61
      0(,1,1(,1(01))) >xbc
      (,1(((,1(,))))= 
     1,10))))=>xbe
     | 11(,1(01)))>xbf
      0,,,1)))  
     | (1  1,,((,0(,))))) =>java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     |(0((,(,0,,))))>java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     |(,0(01,(,1(,)  
     | (0,(1,(0,(1,(0,(1,(1,0))))))) =>       (1,1,1,0,(,(0(11))))) => xc7
     | (1,(1,(0,(1,(0,(1,(1,0))))))) => x6b
     | (0,(0,(1,(1,(0,(1,(10)))) >x6c
     | (1,(0,(1,(1,    |(1,(,0(1,(,0(,))))=> xc9
     |      | (,1(,1(,0(,)))))= xca
     | (1,(1,(1,(1,(0,(1,(1,)))))= x6f
     | (0,(0,(0,(0,(1,(1,(1,0))))))) => x70
     | (,0(,0(1,,1,)))) =>x71
     | (0,(1,(0,(0,(1,(1,(1,0))))))) => x72
     |(,1(0(,1,(,))))=>x73
     | (0,(0,(1,(0,(1,(1,(1,0))))))) => x74
0))) >x75
     | (0,(1,(1,(0,(1|(,0(,01,,0,11)))) >xd1
     | (1,(1,(1,(0,(1,(1,(1,0))))))) => x77
     | (0,(0,(0,(1,(1,(1,(1,0))))))) => x78
     | 0(0(,1(,10))) >x79
     | (0|(,1(0(0(1(,11))) >xd3
     | (1,(1,(0,(1,(1,(1,(1,0))))))) => x7b
     | (0,(0, |(,(0,1(,1(,11))) > 
     | (1,(0,(1 (,((,0(,0(,)))) >x
     | (0,(1,(1,(1,(1,(1,(1,0))))))) => x7e(,1(,(1,011)))) >xd6
     | (,1(11(,1(,))))= x7f
     | (0,(0,(0,(1,(1,(0,(1,1))))))) => xd8
     | (1,(0,(0,(0,(0,(0,(0,1))))))) => x81
      0(,0(,0(,01))) > x82
     | (1,(1,(0,(0,(0,(0,(0,1))))))) => x83
     | (0,(0,(1|(,1(,1(,0(,)))) >xda
     |(,(11,0,11)))) >xdb
     0(1(,0(,0(,))))= x86
      1(1(,0(,0(,))))) =>x87
     | (0,(0,(0,(1,(0,(0,(0,1))))))) => x88
     ||((,1(,1,(,11))))= 
     | (0,(1|(,,1(,1,0,11))) >xdf
     | (1,(1,(0,(1,(0,(0|(,0(,0(,1(,))))=>xe0
     | (0,0(,1(,0(01))) => 
     | (1,(0,(1,(1,(0,|0(,0(,0(111))) >xe2
     ||(,(,00(,1(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (,1(,1(,0(,)))) >x8f
     | (0,(0,(0,(0, 1(11(,0(,11))) =>xe7
     | (1,(0,(0,(0,(1,(0,(0,1))))))) => x91(,00(,0(,11))) >xe8
      (0(,(,0,(1,0(,))))= x92
     | (1,(1,(0,(0,|(,1(,1(,1(,)))) >xea
      (,(,(,0,(1(,01))) >x94
     | (1,|(,0(,1(,1(,))))= xec
     | (0,(1|(,0(,1(,1,(1))) >
     | (1,(1,(1,(0,(1 |(,(1,1,(,0(,(,))))= 
     |(,1(,1,0(,11))) >
     | (1,(0,(0,(1|(,0,0(,1(,11))) >xf0
     | (,0(,,1(,(1))) >xf1
     |(,1(,1(,0(,))))) >x9b
      0((1(,1(,(01))))) >x9c
     | (1,(0,(1,(1,(1,(0,(0,1))))))) => x9d (0,(0(,1(,1(,11))) =>xf4
     | (0,(1,(1,(1,(1,(0,(0,1))))))) => x9e
     |(1(,1,(,1(,01))) = 
     | (0,(0,(0,(0,(0,(1,(0,1)))))|(,1(,0(1,1(,))))= 
      (,0(,0(0,,01))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (,1(,0(,1(,)))) >xa2
     | (1,(1,(0,(0,(0,(1,(0,1) (,1(,1(,1,(11))) =>xfa
     | (0,(0,(1,(0,(0,(1,(0,1))))))) => xa4
     |  (,0(,0(,1,01))) >xa5
    |(,1(,0(,1(,))))) >xa6
     | (1,(1,(1,(0,(0,(1,(0,1))))))) => xa7
     |(,java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      to_bits:) : *bool * bool * ( * (bool*bool)java.lang.StringIndexOutOfBoundsException: Index 97 out of bounds for length 97
     | (0,(1,(00,(0,(0,(0,(0,(0,(0,0)))))))
     | (1,(1,(0,(1,(0,(1,(0,1))) |x01 1(,0(0,(0,(0,0,0))))
     | (0,(0(1(,(,1(,)))) >
     | (1,(0,(|  => (,1(,0,(,(0(00))))
      0(,1(,0(,0,1))))) >xjava.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (1,(1,(1,(1,(0,(1,(0,1))))))) => xaf
     | (0,(0,(0,(0,(1,(1,(0,1))))))) =>      | x06 => (0,(1,(1,(0,(0,(0,(0,0)))))))
      (1,(0,(0(0,(1(1(01))))) => xb1
     |(0,1(0,(0,1,1,0,)))) =>xb2
     | (1,(1,(0,(0,(1,(1,(0,1))))))) => xb3
     | (0,(0,(1,(0,(1,(1,(0,1))))))) => xb4
     | (1,(0,(1,(0,(1,(1,(0,1))))))) => xb5
      (0,1(1(,1(,01)))) >xb6
     | (1,(1,(1,(0,(1,(1,(0,1))))))) => xb7
     |  => (,0(,1(00(,))))
     | (1,(     |x0a= 0(,0(,0(,(0))))
     (0(,0(,1(,01))) = xba
     | (1,(1,(0,(1,(1,(1,(0,1))))))) => xbb
     | (0,(0,(1,(1,(1,(1,( |x0c>(,0(,1(,0(,))))
     | (1,(0(,1,(1(,01))) = xbd
     | (0,(1,(1     |x0e (,1(11(,0(,))))
      1(,1(,1(,(0,))))) >
     | (0,|x10 =>(,0(,0(,0(,))))
     | (1,(0,(0,(0,(0,(0,(1,1))))))) => xc1
     |(0(,(0(,0,0(,))))= xc2
     ||  => 0(,(,0(,0(0,))))
     | (0,(0,(1,(0,(0,(0,(1,1))))))) => xc4
     | (,0,(,(0(0(,11))) >xc5
     | (0,(1,(1,(0,(0,(0,(1,1))))))) => xc6
     | (1,(1,(1,(0,(  => (0(,1(,1(,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
))) = 
     | (1,(0,(0,(1,(0,(0,(1,1)|x17(1(1(,0(,(,00)))
     | (0,(1|x18= 0(,0(,1,,00)))
     | (1,(|x19((,0(,1(,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     || => ((,0(,1(,0,)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (1,(0,(1,(1,(0,(0,(1,1))))))) => xcd
      (,1(,(,(,0(,)))) = xce
     | (1,(1,(1,(1,(0,(0,(1,1)|x1e(,1(,1(,0(,))))
     | (0,(0,(0,(0,(1,(0,(1,1))))))) => xd0
     | (1,(0,(0,(0,(1,(|x1f>(1(,1(,1(,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      (0,1,(0(,1(,11)))) = xd2
     | (      x22= 0(,0(,0(,(,))))
     | (0,(0,(1,(0,(1,(0,(1,1))))))) => xd4
     | (1,|x23 =>(,(,,0(,(,00))))
     | (0,|x24((,1(,0,1(,)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     || x26= (,1(,0(,(,00)))
     | (|x271(,1(,0(,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (1,(0,(|x291(0,0(,0(,00)))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     |  =>1(,0(,0(,00)))
     | (1,(1,(0,(1,(1,(0,(1,1))))))) => xdb
     | (0,(0,(1,(1,(1,(0,(1,1))))))) => xdc
     | (1,(0,(1,(1,(1,(0,(1,1))))))) => xdd
      (0(,((,(1(,11))))= xde
     | (1,(1,(1,(1,(1,(0,(1,1)| =>(,0(,(,0(,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (0,(0,(0|x2f =1(,1(1(,1(,))))
      (,(,0(0,0(,(1,)))) >xe1
     | (0,(1,(0,(0,(0,(1,(1,1))))))) => xe2
     | (1,(1,(0,(0,(0,(1,(1,1))))))) => xe3
      0(,((,0(,(1,)))))= xe4
     | (1,(0,(1,(0,(|x32 = 0(,0(,1(,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (0,|x34 >0(,1(,1(,00))))
      (1(1(,0,,(,(,1))) = 
     | (0,(0, |x36=>(,1(,0(,1(,))))))
     | (1,(0,(0,(1,(0,(1,(1,1))))))) => xe9
     | (0,(1,(0,(|x37((,(,0(,1(,0))))
     | (1,(| 0(,1(,1(,))))
     | (9=>0((,,(,00))))
     | (1,(0,(1,(|x3a0(,0(11(,00)))
     | (0,1(,1(,1,(11)))) =>
     | (1,(1,(1,(1,(0,(1,(1,1))))))) =     x3c >0(,1(,1(,(0)))
     |0(,0(,1(1,11))) >xf0
     (0,(,0(,1(,))))=>xf1
      0(1(00(,1(,)))) > xf2
     | (1,(1,(0,(0,(1,(1,(1,1))))))) => xf3
     | (0,(0,(1,(     x40=>((,00(,0(,))))
      (1,0(1(,1,1(,)))) = xf5
     | (0,1(,0(,1(,1))) >xf6
     | (1,(1,(1,(0,(1,(1,(1,1))))))) => xf7
     | 0(,(0(,1,1(,1))))) =>xf8
     | (1,(0,(0,1(,1(,)))) >java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | (0,|x47,,((,))
     1(((,,,)))  
     | (  = ,,,100(,)))
) >
     |0(,1,1(,1(,))))= java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     1,,1(,(111)))  java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     end.

Definition to_bits :byte) : bool*boolbool( * (bool(boolbool)))))java.lang.StringIndexOutOfBoundsException: Index 97 out of bounds for length 97
  := match b with  =>(,0(0(,1(,10)))
java.lang.StringIndexOutOfBoundsException: Range [11, 5) out of bounds for length 43
     | x01 => (1,(0,(0,(0,(0,(0,(0,0)))))))
     | x02 => (0,(1,(0,(0,(0,(0,(0,0)))))))
     | x03 => (1,(1,(0,(0,(0,(0,(0,0)))))))
     | x04 => (0,(0,(1,(0,(0,(0,(0,0)))))))
     | x05 => (1,(0,(1,(0,(0,(0,(0,0)))))))
     | x06 => (0,(1,(1,(0,(0,(0,(0,0)))))))
     | x07 => (1,(1,(1,(0,(0,(0,(0,0)))))))
     | x08 => (0,(0,(0,(1,(0,(0,(0,0)))))))
     | x09 => (1,(0,(0,(1,(0,(0,(0,0)))))))
     | x0a => (0,(1,(0,(1,(0,(0,(0,0)))))))
      x0b=>(1,1(0,1(0(,00))))
     | x0c => (0,(0,(1,(1,(0,(0,(0,0)))))))
     | x0d => (1,(0,(1,(    |x54>(,0(,0(,0(,0))))
     | x0e(,1(1(,0(,00)))))
     | x0f|x56 = (0(,1(,1,((,))))
     | x10 x57 =>(,1(,0(,0(,))))
     | x11 => (1,(0,(0,(0,(1,(0,(0,0)))))))
     | x12 => (0,(1,(0,(0,(1       => (0,0(,1(,0,(,))))
     | x13 => (1,(1,(0,(0,(1,(0,(0,0)))))))
       => (,0(,0(,0(,))))
     | x15 => (,1(,(1(1(,(10)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
       => (0(,(,0(1,(,00)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x17 => (1,(1,(1|x5e>(0(,1(,0(,))))
     |x5f> (1(,1(,1(,10))))
     | x19 => (1,(0,(0,(1,(1,(0,(0,0)))))))
     | x1a => (0(,0(,0(,10))))
     | x1b  => (,0(,0(,1(1,))))
     | |x62(,1(0(,0(,10))))
     | x1d => (,1(,0(,1(,))))
     | x1e => (0,(1,(1,(1,(1,(0,(0,0)))))))
     | x1f => (1,(,(1,1,1(,(0)))
     | x20 = (0(,0(,0(,00)))
       x66 => 0(,1(,0(,10)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     |x22 0(,0(,0(,(0)))
     | x23 => (1,(1,(0,(0,(0,(1,(0,0)))))))|x69 >(,00(,0(,10)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x24 => (0,(0,(1     | x6b(,1(,1,(,1(,)))))
     | x25 => (1,(0,(1,(0,(0,(1,(0,0)))))))
      x26= (0(1,1(,0(,00)))
     | x27 => (1| x6d>(,0(,1(,1,(,))))
     | x28 => (0,(0,(0,(1,(0,(1,(0,0)))|x6f1(,1(,0(,10))))
     | x29 => (1,(0,(0,(1,(0,(1,(0,0)))))))
     | x2a|x => (0,(,((,1(,10)))
     | x2bx71 = 1,(,0,0(,1(,))))
| = 001(1(((,)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
       =>1,0,,))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
  =0(,11(,1(,))))
| >,,11(,,00)))
     | x30 = 0(,1(,1(,(,0)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x31= 1(,0(,1(,00))))
     | x32 => (0,(1      x80>((,0(,0(,01)))
      x33 =(,1(,0(,1(,))))
     | x34 => (0(,0(,0(,01)))
     | x35  => 1(,0((,0(,))))
     | x36 => (| => (,0(,0,0(,01)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
       => (,1(,(0(,1(,))))
     | x38 => (0,(0,(0,(1,(1,(1,(0,0)))))))
     | x39 => (,,1(,,0(,1)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
       = 0(((,,(00))))
     | x3b => (1,(1,(0,(1,(1,(1,|x8a >(,1(,(,0(,01)))
      x3c = ((,1(1,1(,00))))
     | x3d => (0,0(,(1,0(0(,))))
     | x3e => (0,(1,(1,(1,(1,(1,(0,0)))))))
     | x3f => (1(0,(1,1(,0(1)))java.lang.StringIndexOutOfBoundsException: Range [43, 44) out of bounds for length 43
       => (0(,(0(,0(,10))))
     | x41| => 0(,0(,1(,01)))
     | x42 =|x91(,0(,0,1,(,(01)))))
     | x43 x92 = 0(,0(,1(,01)))))
     | x44x93 =(,1(0(,1(,01)))
     | x45 => (1,(0,(1,(0,(0,(0,(1,0)))))))
       =>(1(,0(,0(,))))
     | x47 x95(,0(,0(1(0,(,))))
     | x48 => (0,(0,(0,(1,(0,(0,(1,0)))))))
      x49 =>1(,0,,0(,)
     | x4a => (0,(1,(0,(1,(0,(0,(1,0)|x971(1,1(,1(,01)))
     | x4b => (1,|x980(,0(,1(,01)))
= 0(,1(,0(,10))))))
 => (,0,(,1(,0(,))))
       => (01(11,,0(,))))
     | x4f => 0(,1(,((,01)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x50 => (0|x9e >0,(,1(,10(,))))
      x51 == (,0(0(,1(,10))))
     | x52 xa0 (,0(,0(,1(,))))
     | x53|xa1,0(,0(,1(,))))
      x54 => 0(,1(,1(,10))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
       => (1,0(,(,1(,10))))))
      x56>(,1(,0(,(,10)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x57 => (1,(1,(1,     |xa7 >(,1(,0(,1(,))))
     | x58 => (0,(0,(0,(1,(1,(0,(1,0)))))))
     |xa8 =(,0(,1(,1(,)))))
     | x5a => (,0(0(,0(1(,)))))
     | x5b 0(,0(1(,1(,))))
     | x5c0(,1(,1(,1,))))
     | x5d => |xac =(,0(,1,0(,01)))))
     |xad(1(,(11(,1(,))))
     | x5f =| xae >(,1(,1(,1(,))))
     | x60 0,0(,0,,1(,))))
     | x61 => (1,(0,(0,(0,(0,(1,(1,0)))))))
     | x62 => (0,(1,(0,(0  => (0(,0,(,(11(,))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
       => (,1(0,0(,1(,))))
     | x64  => (,1(,0(,1(,1))))
     | x65,(0(1,((,1(,))))
     | x66|xb5 >(,0,1(0((,01)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      x67=> (1,1(,0(,1(,0))))
     | x68 => (0,(|xb8= (0(,0(11(,01)))
     | x69| xb9>(,0(0,(,1,1(,))))
     | x6a xba =(,1(,1(,1(0))))
     | x6b => (1,(1,(0,(1,(0,(1,(1,0)))))))
     | x6c => (0,(0,(1,(1,(0,(1, |  => (,10(,1,,01)))
     |x6d= (1(,1(,0(,(,))))
     | x6e => (0,| =>(,0(,1(,1(,))))
     | x6f => (1,(1,(1,(1,(0,(1,(1,0))))))| => 1(,1(,1(,01))))
     | x70 => (0,(0,(0,(0,(1,(1,(1,|xc1 >(1(0(,0(,(,1))))
      x71 => (,0(0(0,1,1(,))))
     | x72 => (0,(1,(0,(0,(1,(1,(1,0)))))))
     | x73 => (1,(1,(0,(0,(1,(1,(1,0)))))))
     | x74 (,0(,0(,1(,0))))
     | x75 => ( => (,01(,0(,11)))
       => (,1(,(,1(1(,))))
     | x77 => (1,(1,(1,(     | xc6 =(0,1(,0(,0(,)))))
     | x78 => (0,(0,(0,(1,(1,(1,(1,0)))))))
       => (1,(,(0,1(1(,10))))
     | x7a => (0,(1,(0,(1,(1,(1,(1,0)))))))
     | x7b => (1,(| >1(,0((0(,)))
     |x7c 01,(,))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | | => ((,1(,0(,11)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
      =01(,1,(,(,(,)))))
     | x7f => (1,(1,(1,(1,(1,(1,(1,0)))))))
     | x80 => (0,(0,(0,(0,(0,(0,(0,1)))))))
     | x81 => (1,(0,(0,(0,(0,(0,(0,1)))))))
     | x82 => (0,(1,     | xd1= (1,(0(0,0,(,(,(,1)))))
     | x83 => (1,(1,(0,(0,(0,(0,(0,1)))))))
     | x84 => (0,(0,(1,(0,(0,(0,(0,1)))))))
      => (1,(0,(1,(,(,(,(,1)))))
     | x86 => (0,(1,(1,(0 xd3 (,1(,0(,0(,))))
     | x87 (1,1,1(,0,(,01))))
     | x88 => (0,(0,(0,(1,(0,(0,(0,1)))))))
     = 10(,1(0(,01)))
     | x8a => (0,(1,(0,(1,(0,(0,(0,1)))))))
     | x8b => (1       =>0,,1(,1(,11)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
       => 0(,1(1(,0(,))))
     | x8d => (1,(0,(1,(1,(0,|  = 0(,0(1,1,0(,))))
       => (0,1(1(,0,0(,))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x8f => (1,(1,(1,(1,(0,(0,(0,1))))))|xdd= (1(,1(1,((,11)))
     | x90 xde >(,1,(,1(,0(,))))
     | x91 => (1,(0,(0,(0,(1,(0,(0,1)))))))
       => (0,(1(,0(,(0,(01))))
     | x93 => (1,(1,(0,(0,(|  =>(,0(00(,1(,))))
      x94= 0,(,1(,1(,01))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x95 =>|xe3>(1((,0(,1(,))))
     ||xe4= 0(,1(,0(,11)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x97 => (1,(1,(1,(0,(1,(0,(0,1)))))))
     | x98 => (0,(0,(0,(1,(1,(0,(0,1)))))))
     | x99 => (1,(0,(0,(1,(1,(0,(0,1)))))))
     | x9a => (0,(1,(0,(1,(1,(0,(0,1)))))))
     | x9b => (1,(1,(0,(1,(1,(0,(0,1)))))))
     | x9c => (0,(0,(1,(1,(1,(0,(0,1)))))))
     | x9d => (1,(0,(1,(1,(1,(0,(0,1)))))))
| x9e> (0(1(,1(1,0(,))))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | x9f => (1,(1,(1,(1,(1,(0,(0,1)))))))
     | xa0 => (0,(0,(0,(0,(0,(1,(0,1)))))))
     | xa1 => (1,(0,(0,(0,(0,(1,(0,1)))))))
     | xa2 => (0,(1,(0,(0,(0,(1,(0,1)))))))
     | xa3 => (1,(1,(0,(0,(0,(1,(0,1)))))))
     | xa4 => (0,(0,(1,(0,(0,(1,(0,1)))))))
     |  xa5=> (1,(0(1(,0(,01)))
     | xa6 => (0,(1,(1,(0     | xe8= (0,(,0(,0(,11)))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | xa7 => (1,(1,(1,(0,(0,     |xea (0(,0(,0(,(11)))
     xa8(,0(,,01(1))
     | xa9 => (1,|xec0(,1(((,1))))
| = 010(,1)))
|  ,(,1010)))
     | xac,(,,,1))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
|>,0((,01(,))java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
     | = 0(01((,1)))
     |      | xf9,,(,1))))
   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.