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<span class="kw">set </span><font color="Maroon" title="c1">F</font> =  the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/>
<a NAME="E1:4_1_1"/>
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of  the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>  holds <br/>(  not <font color="Olive" title="b1">x</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a>  the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a> or <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a>  the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a> or <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a>  the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T12" title="VECTSP_1:th.12">VECTSP_1:12</a></span>;<br/>
<a NAME="E2:4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E3">A1</font></span>: 
 the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a> is  <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_2.html#D1" target="_self" title="VECTSP_2:def.1">Def5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">F</font> =  the   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a> as   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a> ;<br/>
<span class="kw">thus </span><a NAME="E4:4_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a> st <br/>( <font color="Olive">b<sub>1</sub></font> is  <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  &amp;  not <font color="Olive">b<sub>1</sub></font> is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="algstr_0.html#V33" title="ALGSTR_0:attr.33">almost_left_invertible</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4_1_1"><span class="lab"><font color="Green" title="E3">A1</font></span></a></span>; <a class="txt" 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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