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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M1</font>, <font color="Olive" title="b2">M2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b1">M1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">M2</font> holds <br/> <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Olive" title="b2">M2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Olive" title="b1">M1</font></span><br/><b>let </b><font color="Maroon" title="c2">M1</font>, <font color="Maroon" title="c3">M2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">M1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">M2</font> implies  <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Maroon" title="c3">M2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Maroon" title="c2">M1</font> )</span><br/>



<b>assume </b><a NAME="E1:15"/><i><font color="Green" title="E9">A1</font></i>: 
<font color="Maroon" title="c2">M1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">M2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Maroon" title="c3">M2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Maroon" title="c2">M1</font></span><br/>

<b>let </b><font color="Maroon" title="c4">M</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Maroon" title="c3">M2</font> or <font color="Maroon" title="c4">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Maroon" title="c2">M1</font> )</span><br/>

<b>assume </b><a NAME="E2:15"/><i><font color="Green" title="E10">A2</font></i>: 
<font color="Maroon" title="c4">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Maroon" title="c3">M2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Maroon" title="c2">M1</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c5">M</font> = <font color="Maroon" title="c4">M</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<a NAME="E4:15"/>
<font color="Maroon" title="c3">M2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">M</font>
 
<b>by </b><i><a class="txt" href="#E2:15"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="circled1.html#D2" target="_self" title="CIRCLED1:def.2">Def2</a></i>;<br/>
<a NAME="E5:15"/><b>then </b><i><font color="Green" title="E11">A3</font></i>: 
<font color="Maroon" title="c2">M1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">M</font>
 
<b>by </b><i><a class="txt" href="#E1:15"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E6:15"/>
<font color="Maroon" title="c5">M</font> is <a href="rltopsp1.html#V3" title="RLTOPSP1:attr.3">circled</a>
 
<b>by </b><i><a class="txt" href="#E2:15"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="circled1.html#D2" target="_self" title="CIRCLED1:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E7:15"/>
<font color="Maroon" title="c4">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Maroon" title="c2">M1</font>
 <b>by </b><i><a class="txt" href="#E5:15"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="circled1.html#D2" target="_self" title="CIRCLED1:def.2">Def2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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