src/HOL/Library/Euclidean_Space.thy
changeset 30510 4120fc59dd85
parent 30489 5d7d0add1741
child 30549 d2d7874648bd
equal deleted inserted replaced
30509:e19d5b459a61 30510:4120fc59dd85
   132          ORELSE rtac @{thm setsum_0'} i
   132          ORELSE rtac @{thm setsum_0'} i
   133          ORELSE simp_tac (HOL_basic_ss addsimps [@{thm "Cart_eq"}]) i)
   133          ORELSE simp_tac (HOL_basic_ss addsimps [@{thm "Cart_eq"}]) i)
   134    (* THEN' TRY o clarify_tac HOL_cs  THEN' (TRY o rtac @{thm iffI}) *)
   134    (* THEN' TRY o clarify_tac HOL_cs  THEN' (TRY o rtac @{thm iffI}) *)
   135    THEN' asm_full_simp_tac (ss2 addsimps ths)
   135    THEN' asm_full_simp_tac (ss2 addsimps ths)
   136  in
   136  in
   137   Method.thms_args (Method.SIMPLE_METHOD' o vector_arith_tac)
   137   Method.thms_args (SIMPLE_METHOD' o vector_arith_tac)
   138 end
   138 end
   139 *} "Lifts trivial vector statements to real arith statements"
   139 *} "Lifts trivial vector statements to real arith statements"
   140 
   140 
   141 lemma vec_0[simp]: "vec 0 = 0" by (vector vector_zero_def)
   141 lemma vec_0[simp]: "vec 0 = 0" by (vector vector_zero_def)
   142 lemma vec_1[simp]: "vec 1 = 1" by (vector vector_one_def)
   142 lemma vec_1[simp]: "vec 1 = 1" by (vector vector_one_def)
   946   "x \<noteq> y \<longleftrightarrow> \<not> (norm (x - y) \<le> 0)"
   946   "x \<noteq> y \<longleftrightarrow> \<not> (norm (x - y) \<le> 0)"
   947   using norm_ge_zero[of "x - y"] by auto
   947   using norm_ge_zero[of "x - y"] by auto
   948 
   948 
   949 use "normarith.ML"
   949 use "normarith.ML"
   950 
   950 
   951 method_setup norm = {* Method.ctxt_args (Method.SIMPLE_METHOD' o NormArith.norm_arith_tac)
   951 method_setup norm = {* Method.ctxt_args (SIMPLE_METHOD' o NormArith.norm_arith_tac)
   952 *} "Proves simple linear statements about vector norms"
   952 *} "Proves simple linear statements about vector norms"
   953 
   953 
   954 
   954 
   955 
   955 
   956 text{* Hence more metric properties. *}
   956 text{* Hence more metric properties. *}