author wenzelm Mon, 21 Dec 2015 23:24:05 +0100 changeset 61896 f833208ff7c1 parent 61895 e44d5b953f16 child 61897 bc0fc5499085 child 61898 6c7861f783fd
 src/HOL/Library/Sum_of_Squares_Remote.thy file | annotate | diff | comparison | revisions
```--- a/src/HOL/Library/Sum_of_Squares_Remote.thy	Mon Dec 21 21:53:49 2015 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,36 +0,0 @@
-(*  Title:      HOL/Library/Sum_of_Squares_Remote.thy
-    Author:     Amine Chaieb, University of Cambridge
-    Author:     Philipp Meyer, TU Muenchen
-*)
-
-section \<open>Examples with remote CSDP\<close>
-
-theory Sum_of_Squares_Remote
-imports Sum_of_Squares
-begin
-
-lemma "(3::real) * x + 7 * a < 4 & 3 < 2 * x \<Longrightarrow> a < 0"
-  by (sos remote_csdp)
-
-lemma "a1 >= 0 & a2 >= 0 \<and> (a1 * a1 + a2 * a2 = b1 * b1 + b2 * b2 + 2) \<and> (a1 * b1 + a2 * b2 = 0) --> a1 * a2 - b1 * b2 >= (0::real)"
-  by (sos remote_csdp)
-
-lemma "(3::real) * x + 7 * a < 4 & 3 < 2 * x --> a < 0"
-  by (sos remote_csdp)
-
-lemma "(0::real) <= x & x <= 1 & 0 <= y & y <= 1  --> x^2 + y^2 < 1 |(x - 1)^2 + y^2 < 1 | x^2 + (y - 1)^2 < 1 | (x - 1)^2 + (y - 1)^2 < 1"
-  by (sos remote_csdp)
-
-lemma "(0::real) <= x & 0 <= y & 0 <= z & x + y + z <= 3 --> x * y + x * z + y * z >= 3 * x * y * z"
-  by (sos remote_csdp)
-
-lemma "((x::real)^2 + y^2 + z^2 = 1) --> (x + y + z)^2 <= 3"
-  by (sos remote_csdp)
-
-lemma "(w^2 + x^2 + y^2 + z^2 = 1) --> (w + x + y + z)^2 <= (4::real)"
-  by (sos remote_csdp)
-
-lemma "(x::real) >= 1 & y >= 1 --> x * y >= x + y - 1"
-  by (sos remote_csdp)
-
-end```