equal
deleted
inserted
replaced
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 |