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<span class="kw">let </span><font color="Maroon" title="c1">E</font>, <font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">G</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</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="algstr_0.html#L2" title="ALGSTR_0:struct.2">addLoopStr</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">x1</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">E</font><br/>  for <font color="Olive" title="b2">x2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">F</font><br/>  for <font color="Olive" title="b3">x3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c3">G</font> holds   <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1"><a href="prvect_4.html#K2" title="PRVECT_4:func.2">[</a><span class="default"><font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font></span><a href="prvect_4.html#K2" title="PRVECT_4:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prvect_4.html#K2" title="PRVECT_4:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b2">x2</font></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b3">x3</font></span>)</span></span><a href="prvect_4.html#K2" title="PRVECT_4:func.2">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">x1</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">E</font>; <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">x2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">F</font><br/>  for <font color="Olive" title="b2">x3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c3">G</font> holds   <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1"><a href="prvect_4.html#K2" title="PRVECT_4:func.2">[</a><span class="default"><font color="Maroon" title="c4">x1</font>,<font color="Olive" title="b1">x2</font>,<font color="Olive" title="b2">x3</font></span><a href="prvect_4.html#K2" title="PRVECT_4:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prvect_4.html#K2" title="PRVECT_4:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">x2</font></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b2">x3</font></span>)</span></span><a href="prvect_4.html#K2" title="PRVECT_4:func.2">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">x2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">F</font>; <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">x3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c3">G</font> holds   <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1"><a href="prvect_4.html#K2" title="PRVECT_4:func.2">[</a><span class="default"><font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c5">x2</font>,<font color="Olive" title="b1">x3</font></span><a href="prvect_4.html#K2" title="PRVECT_4:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prvect_4.html#K2" title="PRVECT_4:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x2</font></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">x3</font></span>)</span></span><a href="prvect_4.html#K2" title="PRVECT_4:func.2">]</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">x3</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c3">G</font>; <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">  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1"><a href="prvect_4.html#K2" title="PRVECT_4:func.2">[</a><span class="default"><font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">x3</font></span><a href="prvect_4.html#K2" title="PRVECT_4:func.2">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prvect_4.html#K2" title="PRVECT_4:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x2</font></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c6">x3</font></span>)</span></span><a href="prvect_4.html#K2" title="PRVECT_4:func.2">]</a></span></span><br/>







<span class="kw">thus </span> <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1"><a href="prvect_4.html#K2" title="PRVECT_4:func.2">[</a><span class="default"><font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c5">x2</font>,<font color="Maroon" title="c6">x3</font></span><a href="prvect_4.html#K2" title="PRVECT_4:func.2">]</a></span> = 
<span class="p1"><a href="prvect_3.html#K5" title="PRVECT_3:func.5">[</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3"><a href="prvect_3.html#K5" title="PRVECT_3:func.5">[</a><span class="default"><font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c5">x2</font></span><a href="prvect_3.html#K5" title="PRVECT_3:func.5">]</a></span></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c6">x3</font></span>)</span></span><a href="prvect_3.html#K5" title="PRVECT_3:func.5">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="prvect_3.html#T8" onmouseover="rs('prvect_3/T8')" onmouseout="rh()">PRVECT_3:8</a></span>
<br/>.= 
<span class="p1"><a href="prvect_4.html#K2" title="PRVECT_4:func.2">[</a><span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x2</font></span>)</span>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c6">x3</font></span>)</span></span><a href="prvect_4.html#K2" title="PRVECT_4:func.2">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="prvect_3.html#T8" onmouseover="rs('prvect_3/T8')" onmouseout="rh()">PRVECT_3:8</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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