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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</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">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/><span class="kw">let </span><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" 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="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/>



<span class="kw">assume </span><a NAME="E1:15"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<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" 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="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/>

<span class="kw">let </span><font color="Maroon" title="c4">M</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  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/>

<span class="kw">assume </span><a NAME="E2:15"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
<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" 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="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/>

<span class="kw">then </span><span class="kw">reconsider </span><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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="circled1.html#D2" target="_self" onmouseover="rs('circled1/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<a NAME="E5:15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E9">A1</font></span></a></span>;<br/>
<a NAME="E6:15"/>
<font color="Maroon" title="c5">M</font> is  <a href="rltopsp1.html#V3" title="RLTOPSP1:attr.3">circled</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="circled1.html#D2" target="_self" onmouseover="rs('circled1/D2')" onmouseout="rh()">Def2</a></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="circled1.html#D2" target="_self" onmouseover="rs('circled1/D2')" onmouseout="rh()">Def2</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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