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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="bcialg_4.html#NM1" title="BCIALG_4:NM.1">BCI-Algebra_with_Condition(S)</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> holds   <a href="bcialg_4.html#K7" title="BCIALG_4:func.7">Product_S</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</font>,<font color="Olive" title="b3">a3</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Olive" title="b2">a2</font></span>)</span> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Olive" title="b3">a3</font></span><br/><b>let </b><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">a3</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="bcialg_4.html#K7" title="BCIALG_4:func.7">Product_S</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c4">a3</font></span><br/>



<b>thus </b> <a href="bcialg_4.html#K7" title="BCIALG_4:func.7">Product_S</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> = 
<span class="p1">(<span class="default"><a href="bcialg_4.html#K7" title="BCIALG_4:func.7">Product_S</a> <span class="p2"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font></span><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">*&gt;</a></span></span>)</span> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c4">a3</font>
<b>by </b><i><a class="ref" href="bcialg_4.html#T19" target="_self" title="BCIALG_4:th.19">Th19</a>, <a class="ref" href="finsop_1.html#T5" title="FINSOP_1:th.5">FINSOP_1:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="bcialg_4.html#K1" title="BCIALG_4:func.1">*</a> <font color="Maroon" title="c4">a3</font>
<b>by </b><i><a class="ref" href="finsop_1.html#T13" title="FINSOP_1:th.13">FINSOP_1:13</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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