src/ZF/Constructible/L_axioms.thy
changeset 69587 53982d5ec0bb
parent 61798 27f3c10b0b50
child 69593 3dda49e08b9d
equal deleted inserted replaced
69586:9171d1ce5a35 69587:53982d5ec0bb
   128 
   128 
   129 
   129 
   130 text\<open>We must use the meta-existential quantifier; otherwise the reflection
   130 text\<open>We must use the meta-existential quantifier; otherwise the reflection
   131       terms become enormous!\<close>
   131       terms become enormous!\<close>
   132 definition
   132 definition
   133   L_Reflects :: "[i=>o,[i,i]=>o] => prop"  ("(3REFLECTS/ [_,/ _])") where
   133   L_Reflects :: "[i=>o,[i,i]=>o] => prop"  (\<open>(3REFLECTS/ [_,/ _])\<close>) where
   134     "REFLECTS[P,Q] == (\<Or>Cl. Closed_Unbounded(Cl) &
   134     "REFLECTS[P,Q] == (\<Or>Cl. Closed_Unbounded(Cl) &
   135                            (\<forall>a. Cl(a) \<longrightarrow> (\<forall>x \<in> Lset(a). P(x) \<longleftrightarrow> Q(a,x))))"
   135                            (\<forall>a. Cl(a) \<longrightarrow> (\<forall>x \<in> Lset(a). P(x) \<longleftrightarrow> Q(a,x))))"
   136 
   136 
   137 
   137 
   138 theorem Triv_reflection:
   138 theorem Triv_reflection:
   266 subsection\<open>Internalized Formulas for some Set-Theoretic Concepts\<close>
   266 subsection\<open>Internalized Formulas for some Set-Theoretic Concepts\<close>
   267 
   267 
   268 subsubsection\<open>Some numbers to help write de Bruijn indices\<close>
   268 subsubsection\<open>Some numbers to help write de Bruijn indices\<close>
   269 
   269 
   270 abbreviation
   270 abbreviation
   271   digit3 :: i   ("3") where "3 == succ(2)"
   271   digit3 :: i   (\<open>3\<close>) where "3 == succ(2)"
   272 
   272 
   273 abbreviation
   273 abbreviation
   274   digit4 :: i   ("4") where "4 == succ(3)"
   274   digit4 :: i   (\<open>4\<close>) where "4 == succ(3)"
   275 
   275 
   276 abbreviation
   276 abbreviation
   277   digit5 :: i   ("5") where "5 == succ(4)"
   277   digit5 :: i   (\<open>5\<close>) where "5 == succ(4)"
   278 
   278 
   279 abbreviation
   279 abbreviation
   280   digit6 :: i   ("6") where "6 == succ(5)"
   280   digit6 :: i   (\<open>6\<close>) where "6 == succ(5)"
   281 
   281 
   282 abbreviation
   282 abbreviation
   283   digit7 :: i   ("7") where "7 == succ(6)"
   283   digit7 :: i   (\<open>7\<close>) where "7 == succ(6)"
   284 
   284 
   285 abbreviation
   285 abbreviation
   286   digit8 :: i   ("8") where "8 == succ(7)"
   286   digit8 :: i   (\<open>8\<close>) where "8 == succ(7)"
   287 
   287 
   288 abbreviation
   288 abbreviation
   289   digit9 :: i   ("9") where "9 == succ(8)"
   289   digit9 :: i   (\<open>9\<close>) where "9 == succ(8)"
   290 
   290 
   291 
   291 
   292 subsubsection\<open>The Empty Set, Internalized\<close>
   292 subsubsection\<open>The Empty Set, Internalized\<close>
   293 
   293 
   294 definition
   294 definition