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(* Title: HOL/Matrix/cplex/MatrixLP.thy
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ID: $Id$
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Author: Steven Obua
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*)
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theory MatrixLP
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imports Cplex
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begin
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constdefs
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list_case_compute :: "'b list \<Rightarrow> 'a \<Rightarrow> ('b \<Rightarrow> 'b list \<Rightarrow> 'a) \<Rightarrow> 'a"
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"list_case_compute l a f == list_case a f l"
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lemma list_case_compute: "list_case = (\<lambda> (a::'a) f (l::'b list). list_case_compute l a f)"
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apply (rule ext)+
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apply (simp add: list_case_compute_def)
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done
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lemma list_case_compute_empty: "list_case_compute ([]::'b list) = (\<lambda> (a::'a) f. a)"
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apply (rule ext)+
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apply (simp add: list_case_compute_def)
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done
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lemma list_case_compute_cons: "list_case_compute (u#v) = (\<lambda> (a::'a) f. (f (u::'b) v))"
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apply (rule ext)+
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apply (simp add: list_case_compute_def)
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done
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lemma If_True: "(If True) = (\<lambda> x y. x)"
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apply (rule ext)+
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apply auto
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done
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lemma If_False: "(If False) = (\<lambda> x y. y)"
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apply (rule ext)+
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apply auto
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done
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lemma Let_compute: "Let (x::'a) f = ((f x)::'b)"
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by (simp add: Let_def)
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lemma fst_compute: "fst (a::'a, b::'b) = a"
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by auto
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lemma snd_compute: "snd (a::'a, b::'b) = b"
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by auto
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lemma bool1: "(\<not> True) = False" by blast
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lemma bool2: "(\<not> False) = True" by blast
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lemma bool3: "((P\<Colon>bool) \<and> True) = P" by blast
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lemma bool4: "(True \<and> (P\<Colon>bool)) = P" by blast
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lemma bool5: "((P\<Colon>bool) \<and> False) = False" by blast
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lemma bool6: "(False \<and> (P\<Colon>bool)) = False" by blast
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lemma bool7: "((P\<Colon>bool) \<or> True) = True" by blast
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lemma bool8: "(True \<or> (P\<Colon>bool)) = True" by blast
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lemma bool9: "((P\<Colon>bool) \<or> False) = P" by blast
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lemma bool10: "(False \<or> (P\<Colon>bool)) = P" by blast
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lemmas boolarith = bool1 bool2 bool3 bool4 bool5 bool6 bool7 bool8 bool9 bool10
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lemmas float_arith = Float.arith
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lemmas sparse_row_matrix_arith_simps = SparseMatrix.sparse_row_matrix_arith_simps
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lemmas sorted_sp_simps = SparseMatrix.sorted_sp_simps
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lemmas fst_snd_conv = Product_Type.fst_conv Product_Type.snd_conv
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end
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