equal
deleted
inserted
replaced
53 increasing :: "['a => 'b::{order}] => 'a program set" |
53 increasing :: "['a => 'b::{order}] => 'a program set" |
54 --{*Polymorphic in both states and the meaning of @{text "\<le>"}*} |
54 --{*Polymorphic in both states and the meaning of @{text "\<le>"}*} |
55 "increasing f == \<Inter>z. stable {s. z \<le> f s}" |
55 "increasing f == \<Inter>z. stable {s. z \<le> f s}" |
56 |
56 |
57 |
57 |
58 text{*Perhaps equalities.ML shouldn't add this in the first place!*} |
58 text{*Perhaps HOL shouldn't add this in the first place!*} |
59 declare image_Collect [simp del] |
59 declare image_Collect [simp del] |
60 |
60 |
61 subsubsection{*The abstract type of programs*} |
61 subsubsection{*The abstract type of programs*} |
62 |
62 |
63 lemmas program_typedef = |
63 lemmas program_typedef = |
344 by blast |
344 by blast |
345 |
345 |
346 lemma Int_Union_Union: "Union(B) \<inter> A = Union((%C. C \<inter> A)`B)" |
346 lemma Int_Union_Union: "Union(B) \<inter> A = Union((%C. C \<inter> A)`B)" |
347 by blast |
347 by blast |
348 |
348 |
349 text{*Needed for WF reasoning in WFair.ML*} |
349 text{*Needed for WF reasoning in WFair.thy*} |
350 |
350 |
351 lemma Image_less_than [simp]: "less_than `` {k} = greaterThan k" |
351 lemma Image_less_than [simp]: "less_than `` {k} = greaterThan k" |
352 by blast |
352 by blast |
353 |
353 |
354 lemma Image_inverse_less_than [simp]: "less_than^-1 `` {k} = lessThan k" |
354 lemma Image_inverse_less_than [simp]: "less_than^-1 `` {k} = lessThan k" |