<?xml version="1.0"?>
<div class="add">

<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#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>   <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>   <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>   <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>   <a href="clvect_1.html#L1" title="CLVECT_1:struct.1">CLSStruct</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">V1</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="ideal_1.html#V1" title="IDEAL_1:attr.1">add-closed</a>   <a href="lpspacc1.html#V1" title="LPSPACC1:attr.1">multi-closed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>  st  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">V1</font> holds <br/>(  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Olive" title="b1">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b1">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Olive" title="b1">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Olive" title="b1">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Olive" title="b1">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b1">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Olive" title="b1">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Olive" title="b1">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Olive" title="b1">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b1">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Olive" title="b1">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Olive" title="b1">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Olive" title="b1">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b1">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Olive" title="b1">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Olive" title="b1">V1</font></span>)</span> #) is  <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Olive" title="b1">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b1">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Olive" title="b1">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Olive" title="b1">V1</font></span>)</span> #) is  <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Olive" title="b1">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b1">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Olive" title="b1">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Olive" title="b1">V1</font></span>)</span> #) is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Olive" title="b1">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b1">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Olive" title="b1">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Olive" title="b1">V1</font></span>)</span> #) is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">V1</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="ideal_1.html#V1" title="IDEAL_1:attr.1">add-closed</a>   <a href="lpspacc1.html#V1" title="LPSPACC1:attr.1">multi-closed</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"> (  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">V1</font> implies (  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:8"/>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">V1</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="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  )</span><br/>

<a NAME="E2:8"/><span class="kw">then </span>
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#D8" onmouseover="rs('subset_1/D8')" onmouseout="rh()">SUBSET_1:def 8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:8"/>
(  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>  &amp;  <a href="clvect_1.html#G1" title="CLVECT_1:aggr.1">CLSStruct</a>(# <font color="Maroon" title="c2">V1</font>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c2">V1</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="ideal_1.html#K1" title="IDEAL_1:func.1">add|</a> (<font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c1">V</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="lpspacc1.html#K6" title="LPSPACC1:func.6">Mult_</a> <font color="Maroon" title="c2">V1</font></span>)</span> #) is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#T2" target="_self" onmouseover="rs('lpspacc1/T2')" onmouseout="rh()">Th2</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/>


</div>
