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<div><span class="kw">theorem </span><a NAME="T11"><span class="comment"><font color="firebrick">:: NDIFF13:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">v1</font>, <font color="Olive" title="b4">v2</font>, <font color="Olive" title="b5">v3</font> being   <a href="lopban_1.html#V2" title="LOPBAN_1:attr.2">Lipschitzian</a>  <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font><br/>  for <font color="Olive" title="b6">a</font>, <font color="Olive" title="b7">b</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds <br/> ( <font color="Olive" title="b3">v1</font> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">+</a> <font color="Olive" title="b4">v2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">v2</font> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">+</a> <font color="Olive" title="b3">v1</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b3">v1</font> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">+</a> <font color="Olive" title="b4">v2</font></span>)</span> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">+</a> <font color="Olive" title="b5">v3</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b3">v1</font> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v2</font> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">+</a> <font color="Olive" title="b5">v3</font></span>)</span> &amp; <font color="Olive" title="b6">a</font> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">v1</font> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">+</a> <font color="Olive" title="b4">v2</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">a</font> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Olive" title="b3">v1</font></span>)</span> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">a</font> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Olive" title="b4">v2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b6">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b7">b</font></span>)</span> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Olive" title="b3">v1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">a</font> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Olive" title="b3">v1</font></span>)</span> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">b</font> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Olive" title="b3">v1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b6">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b7">b</font></span>)</span> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Olive" title="b3">v1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b6">a</font> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">b</font> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Olive" title="b3">v1</font></span>)</span> )</div></div>
