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<span class="kw">take </span><font color="Maroon" title="c2">T</font> =  <a href="msafree2.html#K7" title="MSAFREE2:func.7">Trivial_Algebra</a> <font color="Maroon" title="c1">S</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">T</font> is  <a href="msafree2.html#V4" title="MSAFREE2:attr.4">finite-yielding</a>  &amp; <font color="Maroon" title="c2">T</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  &amp; <font color="Maroon" title="c2">T</font> is  <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</a>  )</span><br/>

<a NAME="E1:24_1_1"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">T</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msafree2.html#D12" target="_self" onmouseover="rs('msafree2/D12')" onmouseout="rh()">Def12</a></span>;<br/>
<a NAME="E2:24_1_1"/>
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">T</font> is <a href="finset_1.html#V2" title="FINSET_1:attr.2">V39</a>()
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:24_1_1"/>
<font color="Maroon" title="c2">T</font> is  <a href="msafree2.html#V4" title="MSAFREE2:attr.4">finite-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"> ( <font color="Maroon" title="c2">T</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  &amp; <font color="Maroon" title="c2">T</font> is  <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E4:24_1_1"/>
<font color="Maroon" title="c2">T</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1"><span class="lab"><font color="Green" title="E9">A1</font></span></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="c2">T</font> is  <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</a> </span><br/>

<span class="kw">thus </span><a NAME="E5:24_1_1"/>
<font color="Maroon" title="c2">T</font> is  <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</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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