src/FOLP/ex/Propositional_Int.thy
author wenzelm
Sat Jul 25 10:31:27 2009 +0200 (2009-07-25)
changeset 32187 cca43ca13f4f
parent 26408 6964c4799f47
child 35762 af3ff2ba4c54
permissions -rw-r--r--
renamed structure Display_Goal to Goal_Display;
     1 (*  Title:      FOLP/ex/Propositional_Int.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1991  University of Cambridge
     5 *)
     6 
     7 header {* First-Order Logic: propositional examples *}
     8 
     9 theory Propositional_Int
    10 imports IFOLP
    11 begin
    12 
    13 
    14 text "commutative laws of & and | "
    15 lemma "?p : P & Q  -->  Q & P"
    16   by (tactic {* IntPr.fast_tac 1 *})
    17 
    18 lemma "?p : P | Q  -->  Q | P"
    19   by (tactic {* IntPr.fast_tac 1 *})
    20 
    21 
    22 text "associative laws of & and | "
    23 lemma "?p : (P & Q) & R  -->  P & (Q & R)"
    24   by (tactic {* IntPr.fast_tac 1 *})
    25 
    26 lemma "?p : (P | Q) | R  -->  P | (Q | R)"
    27   by (tactic {* IntPr.fast_tac 1 *})
    28 
    29 
    30 text "distributive laws of & and | "
    31 lemma "?p : (P & Q) | R  --> (P | R) & (Q | R)"
    32   by (tactic {* IntPr.fast_tac 1 *})
    33 
    34 lemma "?p : (P | R) & (Q | R)  --> (P & Q) | R"
    35   by (tactic {* IntPr.fast_tac 1 *})
    36 
    37 lemma "?p : (P | Q) & R  --> (P & R) | (Q & R)"
    38   by (tactic {* IntPr.fast_tac 1 *})
    39 
    40 
    41 lemma "?p : (P & R) | (Q & R)  --> (P | Q) & R"
    42   by (tactic {* IntPr.fast_tac 1 *})
    43 
    44 
    45 text "Laws involving implication"
    46 
    47 lemma "?p : (P-->R) & (Q-->R) <-> (P|Q --> R)"
    48   by (tactic {* IntPr.fast_tac 1 *})
    49 
    50 lemma "?p : (P & Q --> R) <-> (P--> (Q-->R))"
    51   by (tactic {* IntPr.fast_tac 1 *})
    52 
    53 lemma "?p : ((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R"
    54   by (tactic {* IntPr.fast_tac 1 *})
    55 
    56 lemma "?p : ~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)"
    57   by (tactic {* IntPr.fast_tac 1 *})
    58 
    59 lemma "?p : (P --> Q & R) <-> (P-->Q)  &  (P-->R)"
    60   by (tactic {* IntPr.fast_tac 1 *})
    61 
    62 
    63 text "Propositions-as-types"
    64 
    65 (*The combinator K*)
    66 lemma "?p : P --> (Q --> P)"
    67   by (tactic {* IntPr.fast_tac 1 *})
    68 
    69 (*The combinator S*)
    70 lemma "?p : (P-->Q-->R)  --> (P-->Q) --> (P-->R)"
    71   by (tactic {* IntPr.fast_tac 1 *})
    72 
    73 
    74 (*Converse is classical*)
    75 lemma "?p : (P-->Q) | (P-->R)  -->  (P --> Q | R)"
    76   by (tactic {* IntPr.fast_tac 1 *})
    77 
    78 lemma "?p : (P-->Q)  -->  (~Q --> ~P)"
    79   by (tactic {* IntPr.fast_tac 1 *})
    80 
    81 
    82 text "Schwichtenberg's examples (via T. Nipkow)"
    83 
    84 lemma stab_imp: "?p : (((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q"
    85   by (tactic {* IntPr.fast_tac 1 *})
    86 
    87 lemma stab_to_peirce: "?p : (((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q)  
    88               --> ((P --> Q) --> P) --> P"
    89   by (tactic {* IntPr.fast_tac 1 *})
    90 
    91 lemma peirce_imp1: "?p : (((Q --> R) --> Q) --> Q)  
    92                --> (((P --> Q) --> R) --> P --> Q) --> P --> Q"
    93   by (tactic {* IntPr.fast_tac 1 *})
    94   
    95 lemma peirce_imp2: "?p : (((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P"
    96   by (tactic {* IntPr.fast_tac 1 *})
    97 
    98 lemma mints: "?p : ((((P --> Q) --> P) --> P) --> Q) --> Q"
    99   by (tactic {* IntPr.fast_tac 1 *})
   100 
   101 lemma mints_solovev: "?p : (P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R"
   102   by (tactic {* IntPr.fast_tac 1 *})
   103 
   104 lemma tatsuta: "?p : (((P7 --> P1) --> P10) --> P4 --> P5)  
   105           --> (((P8 --> P2) --> P9) --> P3 --> P10)  
   106           --> (P1 --> P8) --> P6 --> P7  
   107           --> (((P3 --> P2) --> P9) --> P4)  
   108           --> (P1 --> P3) --> (((P6 --> P1) --> P2) --> P9) --> P5"
   109   by (tactic {* IntPr.fast_tac 1 *})
   110 
   111 lemma tatsuta1: "?p : (((P8 --> P2) --> P9) --> P3 --> P10)  
   112      --> (((P3 --> P2) --> P9) --> P4)  
   113      --> (((P6 --> P1) --> P2) --> P9)  
   114      --> (((P7 --> P1) --> P10) --> P4 --> P5)  
   115      --> (P1 --> P3) --> (P1 --> P8) --> P6 --> P7 --> P5"
   116   by (tactic {* IntPr.fast_tac 1 *})
   117 
   118 end