45 lines
1.4 KiB
Plaintext
45 lines
1.4 KiB
Plaintext
(*
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* Copyright 2014, NICTA
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*
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* This software may be distributed and modified according to the terms of
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* the BSD 2-Clause license. Note that NO WARRANTY is provided.
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* See "LICENSE_BSD2.txt" for details.
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*
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* @TAG(NICTA_BSD)
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*)
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theory WordSetup (* part of non-AFP Word_Lib *)
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imports
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"../Distinct_Prop"
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"../Word_Lib/Word_Lemmas_32"
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begin
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(* Distinct_Prop lemmas that need word lemmas: *)
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lemma distinct_prop_enum:
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"\<lbrakk> \<And>x y. \<lbrakk> x \<le> stop; y \<le> stop; x \<noteq> y \<rbrakk> \<Longrightarrow> P x y \<rbrakk>
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\<Longrightarrow> distinct_prop P [0 :: 'a :: len word .e. stop]"
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apply (simp add: upto_enum_def distinct_prop_map del: upt.simps)
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apply (rule distinct_prop_distinct)
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apply simp
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apply (simp add: less_Suc_eq_le del: upt.simps)
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apply (erule_tac x="of_nat x" in meta_allE)
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apply (erule_tac x="of_nat y" in meta_allE)
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apply (frule_tac y=x in unat_le)
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apply (frule_tac y=y in unat_le)
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apply (erule word_unat.Rep_cases)+
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apply (simp add: toEnum_of_nat[OF unat_lt2p]
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word_le_nat_alt)
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done
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lemma distinct_prop_enum_step:
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"\<lbrakk> \<And>x y. \<lbrakk> x \<le> stop div step; y \<le> stop div step; x \<noteq> y \<rbrakk> \<Longrightarrow> P (x * step) (y * step) \<rbrakk>
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\<Longrightarrow> distinct_prop P [0, step .e. stop]"
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apply (simp add: upto_enum_step_def distinct_prop_map)
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apply (rule distinct_prop_enum)
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apply simp
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done
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end
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