src/ZF/Bool.thy
 changeset 837 778f01546669 parent 799 13aa1e3d8a3a child 1401 0c439768f45c
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836:627f4842b020 837:778f01546669
`     2     ID:         \$Id\$`
`     2     ID:         \$Id\$`
`     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory`
`     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory`
`     4     Copyright   1992  University of Cambridge`
`     4     Copyright   1992  University of Cambridge`
`     5 `
`     5 `
`     6 Booleans in Zermelo-Fraenkel Set Theory `
`     6 Booleans in Zermelo-Fraenkel Set Theory `
`       `
`     7 `
`       `
`     8 2 is equal to bool, but serves a different purpose`
`     7 *)`
`     9 *)`
`     8 `
`    10 `
`     9 Bool = ZF + "simpdata" +`
`    11 Bool = ZF + "simpdata" +`
`    10 consts`
`    12 consts`
`    11     "1"		::      "i"     	("1")`
`    13     "1"		:: "i"     	   ("1")`
`    12     bool        ::      "i"`
`    14     "2"         :: "i"             ("2")`
`    13     cond        ::      "[i,i,i]=>i"`
`    15     bool        :: "i"`
`    14     not		::	"i=>i"`
`    16     cond        :: "[i,i,i]=>i"`
`    15     "and"       ::      "[i,i]=>i"      (infixl 70)`
`    17     not		:: "i=>i"`
`    16     or		::      "[i,i]=>i"      (infixl 65)`
`    18     "and"       :: "[i,i]=>i"      (infixl 70)`
`    17     xor		::      "[i,i]=>i"      (infixl 65)`
`    19     or		:: "[i,i]=>i"      (infixl 65)`
`       `
`    20     xor		:: "[i,i]=>i"      (infixl 65)`
`    18 `
`    21 `
`    19 translations`
`    22 translations`
`    20    "1"  == "succ(0)"`
`    23    "1"  == "succ(0)"`
`       `
`    24    "2"  == "succ(1)"`
`    21 `
`    25 `
`    22 defs`
`    26 defs`
`    23     bool_def	"bool == {0,1}"`
`    27     bool_def	"bool == {0,1}"`
`    24     cond_def	"cond(b,c,d) == if(b=1,c,d)"`
`    28     cond_def	"cond(b,c,d) == if(b=1,c,d)"`
`    25     not_def	"not(b) == cond(b,0,1)"`
`    29     not_def	"not(b) == cond(b,0,1)"`