equal
deleted
inserted
replaced
18 definition |
18 definition |
19 Ord :: "i=>o" where |
19 Ord :: "i=>o" where |
20 "Ord(i) == Transset(i) & (\<forall>x\<in>i. Transset(x))" |
20 "Ord(i) == Transset(i) & (\<forall>x\<in>i. Transset(x))" |
21 |
21 |
22 definition |
22 definition |
23 lt :: "[i,i] => o" (infixl "<" 50) (*less-than on ordinals*) where |
23 lt :: "[i,i] => o" (infixl \<open><\<close> 50) (*less-than on ordinals*) where |
24 "i<j == i\<in>j & Ord(j)" |
24 "i<j == i\<in>j & Ord(j)" |
25 |
25 |
26 definition |
26 definition |
27 Limit :: "i=>o" where |
27 Limit :: "i=>o" where |
28 "Limit(i) == Ord(i) & 0<i & (\<forall>y. y<i \<longrightarrow> succ(y)<i)" |
28 "Limit(i) == Ord(i) & 0<i & (\<forall>y. y<i \<longrightarrow> succ(y)<i)" |
29 |
29 |
30 abbreviation |
30 abbreviation |
31 le (infixl "\<le>" 50) where |
31 le (infixl \<open>\<le>\<close> 50) where |
32 "x \<le> y == x < succ(y)" |
32 "x \<le> y == x < succ(y)" |
33 |
33 |
34 |
34 |
35 subsection\<open>Rules for Transset\<close> |
35 subsection\<open>Rules for Transset\<close> |
36 |
36 |