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<a NAME="E1:85_3_1"/>
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1"><a href="afinsq_1.html#K7" title="AFINSQ_1:func.7">&lt;%</a><span class="default"><font color="Maroon" title="c1">M1</font>,<font color="Maroon" title="c2">M2</font>,<font color="Maroon" title="c3">M3</font></span><a href="afinsq_1.html#K7" title="AFINSQ_1:func.7">%&gt;</a></span> holds <br/><font color="Olive" title="b1">x</font> is   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="85_3_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1"><a href="afinsq_1.html#K7" title="AFINSQ_1:func.7">&lt;%</a><span class="default"><font color="Maroon" title="c1">M1</font>,<font color="Maroon" title="c2">M2</font>,<font color="Maroon" title="c3">M3</font></span><a href="afinsq_1.html#K7" title="AFINSQ_1:func.7">%&gt;</a></span> implies <font color="Maroon" title="c4">x</font> is   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:85_3_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1"><a href="afinsq_1.html#K7" title="AFINSQ_1:func.7">&lt;%</a><span class="default"><font color="Maroon" title="c1">M1</font>,<font color="Maroon" title="c2">M2</font>,<font color="Maroon" title="c3">M3</font></span><a href="afinsq_1.html#K7" title="AFINSQ_1:func.7">%&gt;</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"> <font color="Maroon" title="c4">x</font> is   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> </span><br/>

<a NAME="E2:85_3_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c1">M1</font>,<font color="Maroon" title="c2">M2</font>,<font color="Maroon" title="c3">M3</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T99" onmouseover="rs('afinsq_1/T99')" onmouseout="rh()">AFINSQ_1:99</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:85_3_1_1"/>
<font color="Maroon" title="c4">x</font> is   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D1" onmouseover="rs('enumset1/D1')" onmouseout="rh()">ENUMSET1:def 1</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>
<span class="kw">hence </span><a NAME="E2:85_3_1"/>
<span class="p1"><a href="afinsq_1.html#K7" title="AFINSQ_1:func.7">&lt;%</a><span class="default"><font color="Maroon" title="c1">M1</font>,<font color="Maroon" title="c2">M2</font>,<font color="Maroon" title="c3">M3</font></span><a href="afinsq_1.html#K7" title="AFINSQ_1:func.7">%&gt;</a></span> is  <a href="group_7.html#V1" title="GROUP_7:attr.1">multMagma-yielding</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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