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<a NAME="E1:5_1_1"/>
 ex <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a> st <font color="Olive" title="b1">R</font> is  <a href="field_6.html#V1" title="FIELD_6:attr.1">field-containing</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="5_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">set </span><font color="Maroon" title="c1">F</font> =  the   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>;<br/>
<span class="kw">take </span>
 the   <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">  the   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a> is  <a href="field_6.html#V1" title="FIELD_6:attr.1">field-containing</a> </span><br/>

<a NAME="E1:5_1_1_1"/>
 the   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a> is    <a href="ec_pf_1.html#M1" title="EC_PF_1:mode.1">Subfield</a> of  the   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_4.html#T1" onmouseover="rs('field_4/T1')" onmouseout="rh()">FIELD_4:1</a></span>;<br/>
<a NAME="E2:5_1_1_1"/><span class="kw">then </span>
 the   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a> is    <a href="c0sp1.html#M1" title="C0SP1:mode.1">Subring</a> of  the   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#T12" onmouseover="rs('field_5/T12')" onmouseout="rh()">FIELD_5:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:5_1_1_1"/>
 the   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a> is  <a href="field_6.html#V1" title="FIELD_6:attr.1">field-containing</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"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:5_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a> st <font color="Olive">b<sub>1</sub></font> is  <a href="field_6.html#V1" title="FIELD_6:attr.1">field-containing</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"> verum</span><br/>


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