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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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#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="rlvect_1.html#L1" title="RLVECT_1:struct.1">RLSStruct</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">M</font> being   <a href="rusub_4.html#V2" title="RUSUB_4:attr.2">Affine</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font><br/>  for <font color="Olive" title="b2">v</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> holds  <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <font color="Olive" title="b1">M</font> is  <a href="rusub_4.html#V2" title="RUSUB_4:attr.2">Affine</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">M</font> be   <a href="rusub_4.html#V2" title="RUSUB_4:attr.2">Affine</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</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">v</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> holds  <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <font color="Maroon" title="c2">M</font> is  <a href="rusub_4.html#V2" title="RUSUB_4:attr.2">Affine</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">v</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</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"> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <font color="Maroon" title="c2">M</font> is  <a href="rusub_4.html#V2" title="RUSUB_4:attr.2">Affine</a> </span><br/>





<a NAME="E1:49"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c2">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rusub_4.html#T33" target="_self" onmouseover="rs('rusub_4/T33')" onmouseout="rh()">Th33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:49"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <font color="Maroon" title="c2">M</font> is  <a href="rusub_4.html#V2" title="RUSUB_4:attr.2">Affine</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rusub_4.html#T31" target="_self" onmouseover="rs('rusub_4/T31')" onmouseout="rh()">Th31</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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