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<span class="kw">set </span><font color="Maroon" title="c3">K</font> =  <a href="field_1.html#K4" title="FIELD_1:func.4">KroneckerField</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">p</font>);<br/>
<a NAME="E1:34_1_1"/><span class="lab"><font color="Green" title="E16">E9</font></span>: 
 <a href="field_2.html#K8" title="FIELD_2:func.8">emb_iso</a> <span class="p1">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="field_5.html#E19"><span class="lab"><font color="Green" title="E14">lemdis</font></span></a>, <a class="ref" href="field_2.html#T15" onmouseover="rs('field_2/T15')" onmouseout="rh()">FIELD_2:15</a></span>;<br/>
<a NAME="E2:34_1_1"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="field_4.html#K4" title="FIELD_4:func.4">KroneckerIso</a> <font color="Maroon" title="c2">p</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="field_1.html#K4" title="FIELD_1:func.4">KroneckerField</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">p</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D3" onmouseover="rs('funct_2/D3')" onmouseout="rh()">FUNCT_2:def 3</a></span>;<br/>
<a NAME="E3:34_1_1"/><span class="kw">then </span>
 <a href="field_1.html#K7" title="FIELD_1:func.7">KrRoot</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="field_4.html#K4" title="FIELD_4:func.4">KroneckerIso</a> <font color="Maroon" title="c2">p</font></span>)</span>
 
;<br/>
<a NAME="E4:34_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">E3</font></span>: 
 <a href="field_1.html#K7" title="FIELD_1:func.7">KrRoot</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_4.html#K4" title="FIELD_4:func.4">KroneckerIso</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="field_2.html#K1" title="FIELD_2:func.1">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T32" onmouseover="rs('funct_1/T32')" onmouseout="rh()">FUNCT_1:32</a></span>;<br/>
<a NAME="E5:34_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">E6</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_4.html#K4" title="FIELD_4:func.4">KroneckerIso</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="field_2.html#K1" title="FIELD_2:func.1">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="field_1.html#K7" title="FIELD_1:func.7">KrRoot</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_4.html#K4" title="FIELD_4:func.4">KroneckerIso</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="field_2.html#K1" title="FIELD_2:func.1">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<a NAME="E6:34_1_1"/><span class="lab"><font color="Green" title="E19">E10</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_4.html#K4" title="FIELD_4:func.4">KroneckerIso</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="field_2.html#K1" title="FIELD_2:func.1">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="field_1.html#K7" title="FIELD_1:func.7">KrRoot</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="field_4.html#K4" title="FIELD_4:func.4">KroneckerIso</a> <font color="Maroon" title="c2">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:34_1_1"><span class="lab"><font color="Green" title="E18">E6</font></span></a>, <a class="ref" href="funct_1.html#T33" onmouseover="rs('funct_1/T33')" onmouseout="rh()">FUNCT_1:33</a></span>;<br/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_2.html#K8" title="FIELD_2:func.8">emb_iso</a> <span class="p3">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> = 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ring_4.html#K6" title="RING_4:func.6">Polynom-Ring</a> <font color="Maroon" title="c2">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34_1_1"><span class="lab"><font color="Green" title="E16">E9</font></span></a>, <a class="ref" href="funct_1.html#T33" onmouseover="rs('funct_1/T33')" onmouseout="rh()">FUNCT_1:33</a></span>
<br/>.= 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="field_4.html#K4" title="FIELD_4:func.4">KroneckerIso</a> <font color="Maroon" title="c2">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>
;<br/>
<a NAME="E8:34_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_2.html#K8" title="FIELD_2:func.8">emb_iso</a> <span class="p3">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="field_4.html#K4" title="FIELD_4:func.4">KroneckerIso</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="field_2.html#K1" title="FIELD_2:func.1">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="field_1.html#K7" title="FIELD_1:func.7">KrRoot</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_2.html#K8" title="FIELD_2:func.8">emb_iso</a> <span class="p3">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:34_1_1"><span class="lab"><font color="Green" title="E19">E10</font></span></a>, <a class="ref" href="funct_1.html#T3" onmouseover="rs('funct_1/T3')" onmouseout="rh()">FUNCT_1:3</a></span>;<br/>
<a NAME="E9:34_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_2.html#K8" title="FIELD_2:func.8">emb_iso</a> <span class="p3">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="field_4.html#K4" title="FIELD_4:func.4">KroneckerIso</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="field_2.html#K1" title="FIELD_2:func.1">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="field_1.html#K7" title="FIELD_1:func.7">KrRoot</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="field_2.html#K8" title="FIELD_2:func.8">emb_iso</a> <span class="p2">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T33" onmouseover="rs('funct_1/T33')" onmouseout="rh()">FUNCT_1:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:34_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="field_2.html#K8" title="FIELD_2:func.8">emb_iso</a> <span class="p4">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="field_4.html#K4" title="FIELD_4:func.4">KroneckerIso</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="field_2.html#K1" title="FIELD_2:func.1">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="field_1.html#K7" title="FIELD_1:func.7">KrRoot</a> <font color="Maroon" title="c2">p</font></span>)</span> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p2">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:34_1_1"><span class="lab"><font color="Green" title="E17">E3</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</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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