<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E64">Kr2</font></span>: <a NAME="T41"><span class="comment"><font color="firebrick">:: FIELD_11:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">g</font> being   <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="field_11.html#K5" title="FIELD_11:func.5">nonConstantPolys</a> <font color="Olive" title="b1">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p2">(<span class="default"><a href="field_11.html#K5" title="FIELD_11:func.5">nonConstantPolys</a> <font color="Olive" title="b1">F</font></span>)</span></span>)</span><br/>  for <font color="Olive" title="b3">I</font> being    <a href="field_11.html#M1" title="FIELD_11:mode.1">maxIdeal</a> of <span class="p1">(<span class="default"><a href="field_11.html#K8" title="FIELD_11:func.8">nonConstantPolys</a> (<font color="Olive" title="b2">g</font>,<font color="Olive" title="b1">F</font>)</span>)</span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a> <br/>  for <font color="Olive" title="b4">p</font> being    <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="Olive" title="b1">F</font></span>)</span><br/>  for <font color="Olive" title="b5">m</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>  st <font color="Olive" title="b5">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="field_11.html#K5" title="FIELD_11:func.5">nonConstantPolys</a> <font color="Olive" title="b1">F</font></span>)</span> holds <br/> <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_1.html#K3" title="FIELD_1:func.3">PolyHom</a> <span class="p3">(<span class="default"><a href="field_11.html#K11" title="FIELD_11:func.11">emb</a> (<font color="Olive" title="b1">F</font>,<font color="Olive" title="b3">I</font>,<font color="Olive" title="b2">g</font>)</span>)</span></span>)</span> <a href="field_1.html#K2" title="FIELD_1:func.2">.</a> <font color="Olive" title="b4">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="field_11.html#K12" title="FIELD_11:func.12">KrRoot</a> (<font color="Olive" title="b3">I</font>,<font color="Olive" title="b5">m</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ring_1.html#K1" title="RING_1:func.1">EqRel</a> (<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Polynom-Ring</a> (<span class="p3">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p4">(<span class="default"><a href="field_11.html#K5" title="FIELD_11:func.5">nonConstantPolys</a> <font color="Olive" title="b1">F</font></span>)</span></span>)</span>,<font color="Olive" title="b1">F</font>)</span>)</span>,<font color="Olive" title="b3">I</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="field_11.html#K7" title="FIELD_11:func.7">Poly</a> (<font color="Olive" title="b5">m</font>,<font color="Olive" title="b4">p</font>)</span>)</span>)</div></div>
