equal
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8 theory Fixedpt imports equalities begin |
8 theory Fixedpt imports equalities begin |
9 |
9 |
10 definition |
10 definition |
11 (*monotone operator from Pow(D) to itself*) |
11 (*monotone operator from Pow(D) to itself*) |
12 bnd_mono :: "[i,i=>i]=>o" where |
12 bnd_mono :: "[i,i=>i]=>o" where |
13 "bnd_mono(D,h) \<equiv> h(D)<=D & (\<forall>W X. W<=X \<longrightarrow> X<=D \<longrightarrow> h(W) \<subseteq> h(X))" |
13 "bnd_mono(D,h) \<equiv> h(D)<=D \<and> (\<forall>W X. W<=X \<longrightarrow> X<=D \<longrightarrow> h(W) \<subseteq> h(X))" |
14 |
14 |
15 definition |
15 definition |
16 lfp :: "[i,i=>i]=>i" where |
16 lfp :: "[i,i=>i]=>i" where |
17 "lfp(D,h) \<equiv> \<Inter>({X: Pow(D). h(X) \<subseteq> X})" |
17 "lfp(D,h) \<equiv> \<Inter>({X: Pow(D). h(X) \<subseteq> X})" |
18 |
18 |