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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</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">Z</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   ex <font color="Olive" title="b2">E</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a> st <br/>( <font color="Olive" title="b2">E</font>,<font color="Maroon" title="c1">F</font> <a href="ring_3.html#R2" title="RING_3:pred.2">are_isomorphic</a>  &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">E</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b1">Z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">Z</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">  ex <font color="Olive" title="b1">E</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a> st <br/>( <font color="Olive" title="b1">E</font>,<font color="Maroon" title="c1">F</font> <a href="ring_3.html#R2" title="RING_3:pred.2">are_isomorphic</a>  &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">E</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">r</font> =  the    <a href="field_5.html#M1" title="FIELD_5:mode.1">Renaming</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">Z</font>;<br/>
<span class="kw">take </span><font color="Maroon" title="c4">E</font> =  <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a>  the    <a href="field_5.html#M1" title="FIELD_5:mode.1">Renaming</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">Z</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"> ( <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c1">F</font> <a href="ring_3.html#R2" title="RING_3:pred.2">are_isomorphic</a>  &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">E</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  )</span><br/>

<a NAME="E1:69"/>
 the    <a href="field_5.html#M1" title="FIELD_5:mode.1">Renaming</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">Z</font> <a href="field_5.html#K7" title="FIELD_5:func.7">"</a>  is  <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#T28" target="_self" onmouseover="rs('field_5/T28')" onmouseout="rh()">thiso</a></span>;<br/>
<a NAME="E2:69"/><span class="kw">then </span>
 the    <a href="field_5.html#M1" title="FIELD_5:mode.1">Renaming</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">Z</font> <a href="field_5.html#K7" title="FIELD_5:func.7">"</a>  is  <a href="mod_4.html#V7" title="MOD_4:attr.7">isomorphism</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#T28" target="_self" onmouseover="rs('field_5/T28')" onmouseout="rh()">thiso</a>, <a class="ref" href="mod_4.html#D12" onmouseover="rs('mod_4/D12')" onmouseout="rh()">MOD_4:def 12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:69"/>
<font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c1">F</font> <a href="ring_3.html#R2" title="RING_3:pred.2">are_isomorphic</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">  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">E</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> </span><br/>

<a NAME="E4:69"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a>  the    <a href="field_5.html#M1" title="FIELD_5:mode.1">Renaming</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:69"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">E</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D5" target="_self" onmouseover="rs('field_5/D5')" onmouseout="rh()">defr</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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