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

<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">p</font> being   <a href="field_5.html#V1" title="FIELD_5:attr.1">linear</a>   <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Maroon" title="c1">F</font></span>)</span> holds <br/> (  <a href="ring_4.html#K6" title="RING_4:func.6">Polynom-Ring</a> <font color="Olive" title="b1">p</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 <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="Olive" title="b1">p</font></span>)</span></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 <font color="Maroon" title="c1">F</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="field_5.html#V1" title="FIELD_5:attr.1">linear</a>   <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Maroon" title="c1">F</font></span>)</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"> (  <a href="ring_4.html#K6" title="RING_4:func.6">Polynom-Ring</a> <font color="Maroon" title="c2">p</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 <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> <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="c1">F</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">FP</font> =  <a href="ring_4.html#K6" title="RING_4:func.6">Polynom-Ring</a> <font color="Maroon" title="c2">p</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">f</font> =  <a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font>;<br/>
<a NAME="E1:36"/><span class="lab"><font color="Green" title="E17">H</font></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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">q</font> where <font color="Olive" title="b1">q</font> is   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">F</font> :  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Olive" title="b1">q</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="field_1.html#K1" title="FIELD_1:func.1">deg</a> <font color="Maroon" title="c2">p</font> </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ring_4.html#D8" onmouseover="rs('ring_4/D8')" onmouseout="rh()">RING_4:def 8</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E18">A</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="36_1"><span class="kw">now </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">  for <font color="Olive" title="b1">o</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  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> holds <br/><font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN: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_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">o</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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"> ( <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  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> implies <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN: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_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:36_1"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  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>
 ; <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="c5">o</font> <a href="hidden.html#R2" title="HIDDEN: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_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">q</font> being   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">F</font><span class="kw"> such that </span><br/><a NAME="E3:36_1"/><span class="lab"><font color="Green" title="E19">B</font></span>: 
( <font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font> &amp;  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c6">q</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="field_1.html#K1" title="FIELD_1:func.1">deg</a> <font color="Maroon" title="c2">p</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E17">H</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c7">q</font> = <font color="Maroon" title="c6">q</font> as    <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Maroon" title="c1">F</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom3.html#D10" onmouseover="rs('polynom3/D10')" onmouseout="rh()">POLYNOM3:def 10</a></span>;<br/><a NAME="E5:36_1"/>
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c7">q</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1"><span class="lab"><font color="Green" title="E19">B</font></span></a>, <a class="ref" href="field_5.html#D1" target="_self" onmouseover="rs('field_5/D1')" onmouseout="rh()">defl</a></span>;<br/><a NAME="E6:36_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c7">q</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T7" onmouseover="rs('int_1/T7')" onmouseout="rh()">INT_1:7</a></span>;<br/><a NAME="E7:36_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c7">q</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" onmouseover="rs('xreal_1/T9')" onmouseout="rh()">XREAL_1:9</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font><span class="kw"> such that </span><br/><a NAME="E9:36_1"/><span class="lab"><font color="Green" title="E20">C</font></span>: 
<font color="Maroon" title="c7">q</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">a</font> <a href="ring_4.html#K2" title="RING_4:func.2">|</a> <font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ring_4.html#T20" onmouseover="rs('ring_4/T20')" onmouseout="rh()">RING_4:20</a>, <a class="ref" href="ring_4.html#D4" onmouseover="rs('ring_4/D4')" onmouseout="rh()">RING_4:def 4</a></span>;<br/><a NAME="E10:36_1"/><span class="lab"><font color="Green" title="E21">D</font></span>: 
<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> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1"><span class="lab"><font color="Green" title="E19">B</font></span></a>, <a class="txt" href="#E9:36_1"><span class="lab"><font color="Green" title="E20">C</font></span></a>, <a class="ref" href="field_5.html#D2" target="_self" onmouseover="rs('field_5/D2')" onmouseout="rh()">defch</a></span>;<br/><a NAME="E11:36_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</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> <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="c1">F</font>
 <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/><span class="kw">hence </span><a NAME="E12:36_1"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN: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_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:36_1"><span class="lab"><font color="Green" title="E21">D</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</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><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E19">X</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="36_2"><span class="kw">now </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">  for <font color="Olive" title="b1">o</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN: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_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span> holds <br/><font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  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></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">o</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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"> ( <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN: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_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</span> implies <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  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><br/><span class="kw">assume </span><a NAME="E1:36_2"/><span class="lab"><font color="Green" title="E20">B</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN: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_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font></span>)</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"> <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  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><br/><a NAME="E2:36_2"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  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="ref" href="relat_1.html#D19" onmouseover="rs('relat_1/D19')" onmouseout="rh()">RELAT_1:def 19</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_2"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  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="#E1:36_2"><span class="lab"><font color="Green" title="E20">B</font></span></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><span class="kw">end;</span></div>
<a NAME="E4:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">B</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</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> <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="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="#E2:36"><span class="lab"><font color="Green" title="E18">A</font></span></a>, <a class="ref" href="tarski.html#T2" onmouseover="rs('tarski/T2')" onmouseout="rh()">TARSKI:2</a></span>;<br/>
<a NAME="E5:36"/>
(  <a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font> is  <a href="mod_4.html#V3" title="MOD_4:attr.3">monomorphism</a>  &amp;  <a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <font color="Maroon" title="c2">p</font> 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="#E3:36"><span class="lab"><font color="Green" title="E19">X</font></span></a>, <a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E18">A</font></span></a>, <a class="ref" href="tarski.html#T2" onmouseover="rs('tarski/T2')" onmouseout="rh()">TARSKI:2</a></span>;<br/>
<a NAME="E6:36"/><span class="kw">then </span>
<font color="Maroon" title="c1">F</font>, <a href="ring_4.html#K6" title="RING_4:func.6">Polynom-Ring</a> <font color="Maroon" title="c2">p</font> <a href="ring_3.html#R2" title="RING_3:pred.2">are_isomorphic</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E7:36"/>
 <a href="ring_4.html#K6" title="RING_4:func.6">Polynom-Ring</a> <font color="Maroon" title="c2">p</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 <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> <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="c1">F</font></span><br/>

<a NAME="E8:36"/><span class="lab"><font color="Green" title="E21">X</font></span>: 
(  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <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> <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="ring_4.html#K6" title="RING_4:func.6">Polynom-Ring</a> <font color="Maroon" title="c2">p</font></span>)</span> &amp;  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">F</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="c1">F</font> )
 
;<br/>
<span class="kw">thus </span> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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> = 
 <a href="field_2.html#K2" title="FIELD_2:func.2">carr</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_2.html#D7" onmouseover="rs('field_2/D7')" onmouseout="rh()">FIELD_2:def 7</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</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></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36"><span class="lab"><font color="Green" title="E21">X</font></span></a>, <a class="ref" href="field_2.html#D2" onmouseover="rs('field_2/D2')" onmouseout="rh()">FIELD_2:def 2</a></span>
<br/>.= 
<a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36"><span class="lab"><font color="Green" title="E20">B</font></span></a>, <a class="ref" href="xboole_1.html#T37" onmouseover="rs('xboole_1/T37')" onmouseout="rh()">XBOOLE_1:37</a></span>
<br/>.= 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</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"> verum</span><br/>


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