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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font>, <font color="Maroon" title="c3">U</font> be  non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c4">R1</font> be   <a href="ndiff_1.html#NM1" title="NDIFF_1:NM.1">REST</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>;<br/>







<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c4">R1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">T</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">R2</font> be   <a href="ndiff_1.html#NM1" title="NDIFF_1:NM.1">REST</a> of <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">U</font>;<br/>

<b>assume </b><a NAME="E2:16"/><i><font color="Green" title="E11">A2</font></i>: 
<font color="Maroon" title="c5">R2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">U</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c6">L1</font> be  <a href="lopban_1.html#V3" title="LOPBAN_1:attr.3">bounded</a> <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>;<br/><b>let </b><font color="Maroon" title="c7">L2</font> be  <a href="lopban_1.html#V3" title="LOPBAN_1:attr.3">bounded</a> <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">U</font>;<br/>



<a NAME="E3:16"/><i><font color="Green" title="E12">A3</font></i>: 
<font color="Maroon" title="c7">L2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">R1</font> is   <a href="ndiff_1.html#NM1" title="NDIFF_1:NM.1">REST</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>
 
<b>by </b><i><a class="ref" href="ndiff_2.html#T9" target="_self" title="NDIFF_2:th.9">Th9</a></i>;<br/>
<a NAME="E4:16"/>
<font color="Maroon" title="c5">R2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">L1</font> <a href="vfunct_1.html#K1" title="VFUNCT_1:func.1">+</a> <font color="Maroon" title="c4">R1</font></span>)</span> is   <a href="ndiff_1.html#NM1" title="NDIFF_1:NM.1">REST</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E1:16"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="ndiff_2.html#E2:16"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="ndiff_2.html#T11" target="_self" title="NDIFF_2:th.11">Th11</a></i>;<br/>
<b>hence </b><a NAME="E5:16"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">L2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">R1</font></span>)</span> <a href="vfunct_1.html#K1" title="VFUNCT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">R2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">L1</font> <a href="vfunct_1.html#K1" title="VFUNCT_1:func.1">+</a> <font color="Maroon" title="c4">R1</font></span>)</span></span>)</span> is   <a href="ndiff_1.html#NM1" title="NDIFF_1:NM.1">REST</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">U</font>
 <b>by </b><i><a class="txt" href="ndiff_2.html#E3:16"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="ndiff_1.html#T33" title="NDIFF_1:th.33">NDIFF_1:33</a></i>;<br/>


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