src/Sequents/ILL_predlog.thy
author haftmann
Fri Jun 19 21:08:07 2009 +0200 (2009-06-19)
changeset 31726 ffd2dc631d88
parent 22895 adc529c89281
child 35054 a5db9779b026
permissions -rw-r--r--
merged
wenzelm@21426
     1
(* $Id$ *)
wenzelm@21426
     2
wenzelm@21426
     3
theory ILL_predlog
wenzelm@21426
     4
imports ILL
wenzelm@21426
     5
begin
wenzelm@21426
     6
wenzelm@21426
     7
typedecl plf
wenzelm@21426
     8
wenzelm@21426
     9
consts
wenzelm@21426
    10
  conj :: "[plf,plf] => plf"   (infixr "&" 35)
wenzelm@21426
    11
  disj :: "[plf,plf] => plf"   (infixr "|" 35)
wenzelm@21426
    12
  impl :: "[plf,plf] => plf"   (infixr ">" 35)
wenzelm@21426
    13
  eq :: "[plf,plf] => plf"   (infixr "=" 35)
wenzelm@21426
    14
  ff    :: "plf"
wenzelm@21426
    15
wenzelm@21426
    16
  PL    :: "plf => o"      ("[* / _ / *]" [] 100)
wenzelm@21426
    17
wenzelm@22895
    18
syntax
wenzelm@22895
    19
  "_NG" :: "plf => plf"   ("- _ " [50] 55)
wenzelm@22895
    20
wenzelm@21426
    21
translations
wenzelm@21426
    22
wenzelm@21426
    23
  "[* A & B *]" == "[*A*] && [*B*]"
wenzelm@21426
    24
  "[* A | B *]" == "![*A*] ++ ![*B*]"
wenzelm@21426
    25
  "[* - A *]"   == "[*A > ff*]"
wenzelm@21426
    26
  "[* ff *]"    == "0"
wenzelm@21426
    27
  "[* A = B *]" => "[* (A > B) & (B > A) *]"
wenzelm@21426
    28
wenzelm@21426
    29
  "[* A > B *]" == "![*A*] -o [*B*]"
wenzelm@21426
    30
wenzelm@21426
    31
(* another translations for linear implication:
wenzelm@21426
    32
  "[* A > B *]" == "!([*A*] -o [*B*])" *)
wenzelm@21426
    33
wenzelm@21426
    34
(* from [kleene 52] pp 118,119 *)
wenzelm@21426
    35
wenzelm@21426
    36
lemma k49a: "|- [* A > ( - ( - A)) *]"
wenzelm@21427
    37
  by best_safe
wenzelm@21426
    38
wenzelm@21426
    39
lemma k49b: "|- [*( - ( - ( - A))) = ( - A)*]"
wenzelm@21427
    40
  by best_safe
wenzelm@21426
    41
wenzelm@21426
    42
lemma k49c: "|- [* (A | - A) > ( - - A = A) *]"
wenzelm@21427
    43
  by best_safe
wenzelm@21426
    44
wenzelm@21426
    45
lemma k50a: "|- [* - (A = - A) *]"
wenzelm@21427
    46
  by best_power
wenzelm@21426
    47
wenzelm@21426
    48
lemma k51a: "|- [* - - (A | - A) *]"
wenzelm@21427
    49
  by best_safe
wenzelm@21426
    50
wenzelm@21426
    51
lemma k51b: "|- [* - - (- - A > A) *]"
wenzelm@21427
    52
  by best_power
wenzelm@21426
    53
wenzelm@21426
    54
lemma k56a: "|- [* (A | B) > - (- A & - B) *]"
wenzelm@21427
    55
  by best_safe
wenzelm@21426
    56
wenzelm@21426
    57
lemma k56b: "|- [* (-A | B) > - (A & -B) *]"
wenzelm@21427
    58
  by best_safe
wenzelm@21426
    59
wenzelm@21426
    60
lemma k57a: "|- [* (A & B) > - (-A | -B) *]"
wenzelm@21427
    61
  by best_safe
wenzelm@21426
    62
wenzelm@21426
    63
lemma k57b: "|- [* (A & -B) > -(-A | B) *]"
wenzelm@21427
    64
  by best_power
wenzelm@21426
    65
wenzelm@21426
    66
lemma k58a: "|- [* (A > B) > - (A & -B) *]"
wenzelm@21427
    67
  by best_safe
wenzelm@21426
    68
wenzelm@21426
    69
lemma k58b: "|- [* (A > -B) = -(A & B) *]"
wenzelm@21427
    70
  by best_safe
wenzelm@21426
    71
wenzelm@21426
    72
lemma k58c: "|- [* - (A & B) = (- - A > - B) *]"
wenzelm@21427
    73
  by best_safe
wenzelm@21426
    74
wenzelm@21426
    75
lemma k58d: "|- [* (- - A > - B) = - - (-A | -B) *]"
wenzelm@21427
    76
  by best_safe
wenzelm@21426
    77
wenzelm@21426
    78
lemma k58e: "! [* - -B > B *] |- [* (- -A > B) = (A > B) *]"
wenzelm@21427
    79
  by best_safe
wenzelm@21426
    80
wenzelm@21426
    81
lemma k58f: "! [* - -B > B *] |- [* (A > B) = - (A & -B) *]"
wenzelm@21427
    82
  by best_safe
wenzelm@21426
    83
wenzelm@21426
    84
lemma k58g: "|- [* (- -A > B) > - (A & -B) *]"
wenzelm@21427
    85
  by best_safe
wenzelm@21426
    86
wenzelm@21426
    87
lemma k59a: "|- [* (-A | B) > (A > B) *]"
wenzelm@21427
    88
  by best_safe
wenzelm@21426
    89
wenzelm@21426
    90
lemma k59b: "|- [* (A > B) > - - (-A | B) *]"
wenzelm@21427
    91
  by best_power
wenzelm@21426
    92
wenzelm@21426
    93
lemma k59c: "|- [* (-A > B) > - -(A | B) *]"
wenzelm@21427
    94
  by best_power
wenzelm@21426
    95
wenzelm@21426
    96
lemma k60a: "|- [* (A & B) > - (A > -B) *]"
wenzelm@21427
    97
  by best_safe
wenzelm@21426
    98
wenzelm@21426
    99
lemma k60b: "|- [* (A & -B) > - (A > B) *]"
wenzelm@21427
   100
  by best_safe
wenzelm@21426
   101
wenzelm@21426
   102
lemma k60c: "|- [* ( - - A & B) > - (A > -B) *]"
wenzelm@21427
   103
  by best_safe
wenzelm@21426
   104
wenzelm@21426
   105
lemma k60d: "|- [* (- - A & - B) = - (A > B) *]"
wenzelm@21427
   106
  by best_safe
wenzelm@21426
   107
wenzelm@21426
   108
lemma k60e: "|- [* - (A > B) = - (-A | B) *]"
wenzelm@21427
   109
  by best_safe
wenzelm@21426
   110
wenzelm@21426
   111
lemma k60f: "|- [* - (-A | B) = - - (A & -B) *]"
wenzelm@21427
   112
  by best_safe
wenzelm@21426
   113
wenzelm@21426
   114
lemma k60g: "|- [* - - (A > B) = - (A & -B) *]"
wenzelm@21427
   115
  by best_power
wenzelm@21426
   116
wenzelm@21426
   117
lemma k60h: "|- [* - (A & -B) = (A > - -B) *]"
wenzelm@21427
   118
  by best_safe
wenzelm@21426
   119
wenzelm@21426
   120
lemma k60i: "|- [* (A > - -B) = (- -A > - -B) *]"
wenzelm@21427
   121
  by best_safe
wenzelm@21426
   122
wenzelm@21426
   123
lemma k61a: "|- [* (A | B) > (-A > B) *]"
wenzelm@21427
   124
  by best_safe
wenzelm@21426
   125
wenzelm@21426
   126
lemma k61b: "|- [* - (A | B) = - (-A > B) *]"
wenzelm@21427
   127
  by best_power
wenzelm@21426
   128
wenzelm@21426
   129
lemma k62a: "|- [* (-A | -B) > - (A & B) *]"
wenzelm@21427
   130
  by best_safe
wenzelm@21426
   131
wenzelm@21426
   132
end