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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="prvect_2.html#NM3" title="PRVECT_2:NM.3">RealNormSpace-Sequence</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Z</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">f</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="lopban_9.html#K10" title="LOPBAN_9:func.10">R_NormSpace_of_BoundedBilinearOperators</a> (<span class="p2">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span>,<font color="Olive" title="b1">Z</font>)</span>)</span> holds  <font color="Olive" title="b2">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ndiff_7.html#K3" title="NDIFF_7:func.3">IsoCPNrSP</a> (<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span>)</span>)</span> <a href="ndiff_7.html#K4" title="NDIFF_7:func.4">"</a></span>)</span> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="lopban10.html#K18" title="LOPBAN10:func.18">R_NormSpace_of_BoundedMultilinearOperators</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<font color="Olive" title="b1">Z</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">Z</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="lopban_9.html#K10" title="LOPBAN_9:func.10">R_NormSpace_of_BoundedBilinearOperators</a> (<span class="p2">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span>,<font color="Maroon" title="c3">Z</font>)</span>)</span> holds  <font color="Olive" title="b1">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ndiff_7.html#K3" title="NDIFF_7:func.3">IsoCPNrSP</a> (<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span>)</span>)</span> <a href="ndiff_7.html#K4" title="NDIFF_7:func.4">"</a></span>)</span> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="lopban10.html#K18" title="LOPBAN10:func.18">R_NormSpace_of_BoundedMultilinearOperators</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<font color="Maroon" title="c3">Z</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="lopban_9.html#K10" title="LOPBAN_9:func.10">R_NormSpace_of_BoundedBilinearOperators</a> (<span class="p2">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span>,<font color="Maroon" title="c3">Z</font>)</span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ndiff_7.html#K3" title="NDIFF_7:func.3">IsoCPNrSP</a> (<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span>)</span>)</span> <a href="ndiff_7.html#K4" title="NDIFF_7:func.4">"</a></span>)</span> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="lopban10.html#K18" title="LOPBAN10:func.18">R_NormSpace_of_BoundedMultilinearOperators</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<font color="Maroon" title="c3">Z</font>)</span>)</span></span><br/>





<a NAME="E1:39"/>
<font color="Maroon" title="c4">f</font> is   <a href="lopban_9.html#V1" title="LOPBAN_9:attr.1">Lipschitzian</a>  <a href="lopban_8.html#NM2" title="LOPBAN_8:NM.2">BilinearOperator</a> of <span class="p1">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span>,<font color="Maroon" title="c3">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lopban_9.html#D4" onmouseover="rs('lopban_9/D4')" onmouseout="rh()">LOPBAN_9:def 4</a></span>;<br/>
<a NAME="E2:39"/><span class="kw">then </span>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ndiff_7.html#K3" title="NDIFF_7:func.3">IsoCPNrSP</a> (<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span>)</span>)</span> <a href="ndiff_7.html#K4" title="NDIFF_7:func.4">"</a></span>)</span> is   <a href="lopban10.html#V3" title="LOPBAN10:attr.3">Lipschitzian</a>  <a href="lopban10.html#NM2" title="LOPBAN10:NM.2">MultilinearOperator</a> of <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<font color="Maroon" title="c3">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lopban12.html#T13" onmouseover="rs('lopban12/T13')" onmouseout="rh()">LOPBAN12:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:39"/>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ndiff_7.html#K3" title="NDIFF_7:func.3">IsoCPNrSP</a> (<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span>)</span>)</span> <a href="ndiff_7.html#K4" title="NDIFF_7:func.4">"</a></span>)</span> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="lopban10.html#K18" title="LOPBAN10:func.18">R_NormSpace_of_BoundedMultilinearOperators</a> (<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p3">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<font color="Maroon" title="c3">Z</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lopban10.html#D11" onmouseover="rs('lopban10/D11')" onmouseout="rh()">LOPBAN10:def 11</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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