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<div><span class="kw">theorem </span><a NAME="T29"><span class="comment"><font color="firebrick">:: CAYLDICK:29</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">N</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="algstr_0.html#V31" title="ALGSTR_0:attr.31">almost_right_cancelable</a>   <a href="algstr_0.html#V33" title="ALGSTR_0:attr.33">almost_left_invertible</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">vector-distributive</a>   <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">scalar-distributive</a>   <a href="rlvect_1.html#V7" title="RLVECT_1:attr.7">scalar-associative</a>   <a href="rlvect_1.html#V8" title="RLVECT_1:attr.8">scalar-unital</a>   <a href="funcsdom.html#V2" title="FUNCSDOM:attr.2">vector-associative</a>   <a href="normsp_0.html#V3" title="NORMSP_0:attr.3">discerning</a>   <a href="normsp_0.html#V4" title="NORMSP_0:attr.4">reflexive</a>   <a href="normsp_1.html#V2" title="NORMSP_1:attr.2">RealNormSpace-like</a>   <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="lopban_2.html#V3" title="LOPBAN_2:attr.3">Banach_Algebra-like_2</a>   <a href="lopban_2.html#V4" title="LOPBAN_2:attr.4">Banach_Algebra-like_3</a>   <a href="cayldick.html#V3" title="CAYLDICK:attr.3">well-conjugated</a>   <a href="cayldick.html#V4" title="CAYLDICK:attr.4">add-conjugative</a>   <a href="cayldick.html#L1" title="CAYLDICK:struct.1">ConjNormAlgStr</a> <br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">N</font>  st (  not <font color="Olive" title="b2">a</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  or  not <font color="Olive" title="b3">b</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  ) &amp; <span class="p1"><a href="cayldick.html#K5" title="CAYLDICK:func.5">&lt;%</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="cayldick.html#K5" title="CAYLDICK:func.5">%&gt;</a></span> is  <a href="algstr_0.html#V17" title="ALGSTR_0:attr.17">right_mult-cancelable</a>  &amp; <span class="p1"><a href="cayldick.html#K5" title="CAYLDICK:func.5">&lt;%</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="cayldick.html#K5" title="CAYLDICK:func.5">%&gt;</a></span> is  <a href="algstr_0.html#V23" title="ALGSTR_0:attr.23">left_invertible</a>  holds <br/> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">/</a> <span class="p1"><a href="cayldick.html#K5" title="CAYLDICK:func.5">&lt;%</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="cayldick.html#K5" title="CAYLDICK:func.5">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cayldick.html#K5" title="CAYLDICK:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b2">a</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><span class="p0"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b3">b</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">a</font> <a href="cayldick.html#K2" title="CAYLDICK:func.2">*'</a></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b2">a</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><span class="p0"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b3">b</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b3">b</font></span>)</span></span>)</span></span><a href="cayldick.html#K5" title="CAYLDICK:func.5">%&gt;</a></span></div></div>
