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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="lopban_1.html#K10" title="LOPBAN_1:func.10">BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> holds <br/> ( <font color="Olive" title="b1">f</font> <a href="lopban_2.html#K3" title="LOPBAN_2:func.3">*</a> <span class="p1">(<span class="default"><a href="lopban_2.html#K6" title="LOPBAN_2:func.6">FuncUnit</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> &amp; <span class="p1">(<span class="default"><a href="lopban_2.html#K6" title="LOPBAN_2:func.6">FuncUnit</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="lopban_2.html#K3" title="LOPBAN_2:func.3">*</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="lopban_1.html#K10" title="LOPBAN_1:func.10">BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> <a href="lopban_2.html#K3" title="LOPBAN_2:func.3">*</a> <span class="p1">(<span class="default"><a href="lopban_2.html#K6" title="LOPBAN_2:func.6">FuncUnit</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> &amp; <span class="p1">(<span class="default"><a href="lopban_2.html#K6" title="LOPBAN_2:func.6">FuncUnit</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="lopban_2.html#K3" title="LOPBAN_2:func.3">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> )</span><br/>



<a NAME="E1:14"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> is   <a href="lopban_1.html#V2" title="LOPBAN_1:attr.2">bounded</a>  <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lopban_2.html#T3" target="_self" title="LOPBAN_2:th.3">Th3</a></span>;<br/>
<a NAME="E2:14"/><span class="kw">then </span>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="lopban_1.html#K10" title="LOPBAN_1:func.10">BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lopban_1.html#D10" title="LOPBAN_1:def.10">LOPBAN_1:def 10</a></span>;<br/>
<a NAME="E3:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A1</font></span>: 
 <a href="lopban_1.html#K13" title="LOPBAN_1:func.13">modetrans</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font></span>)</span>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lopban_1.html#D12" title="LOPBAN_1:def.12">LOPBAN_1:def 12</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c2">f</font> <a href="lopban_2.html#K3" title="LOPBAN_2:func.3">*</a> <span class="p1">(<span class="default"><a href="lopban_2.html#K6" title="LOPBAN_2:func.6">FuncUnit</a> <font color="Maroon" title="c1">X</font></span>)</span> = 
 <a href="lopban_1.html#K13" title="LOPBAN_1:func.13">modetrans</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lopban_2.html#T6" target="_self" title="LOPBAN_2:th.6">Th6</a></span>
<br/>.= 
<font color="Maroon" title="c2">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lopban_1.html#D12" title="LOPBAN_1:def.12">LOPBAN_1:def 12</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="lopban_2.html#K6" title="LOPBAN_2:func.6">FuncUnit</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="lopban_2.html#K3" title="LOPBAN_2:func.3">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font></span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="lopban_2.html#K6" title="LOPBAN_2:func.6">FuncUnit</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="lopban_2.html#K3" title="LOPBAN_2:func.3">*</a> <font color="Maroon" title="c2">f</font> = 
 <a href="lopban_1.html#K13" title="LOPBAN_1:func.13">modetrans</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="lopban_2.html#T6" target="_self" title="LOPBAN_2:th.6">Th6</a></span>
<br/>.= 
<font color="Maroon" title="c2">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lopban_1.html#D12" title="LOPBAN_1:def.12">LOPBAN_1:def 12</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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