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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_1_1_1"/>
(  not <font color="Maroon">c<sub>1</sub></font> is <a href="msualg_1.html#V2">void</a> or <font color="Maroon">c<sub>1</sub></font> is <a href="msualg_1.html#V2">void</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_1_1_1_1"><b>case </b></a><a NAME="E1:25_1_1_1_1"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="msualg_1.html#V2">void</a>
 ;<br/><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>assume </b><a NAME="E2:25_1_1_1_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>4</sub></font>;<br/><b>assume </b><a NAME="E3:25_1_1_1_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">c<sub>5</sub></font> <b>by </b><i><a class="txt" href="equation.html#E2:25_1_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="msualg_2.html#D18">MSUALG_2:def 18</a></i>;<br/><a NAME="E5:25_1_1_1_1"/>
 <a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="equation.html#E2:25_1_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="equation.html#E3:25_1_1_1_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="extens_1.html#T22">EXTENS_1:22</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as    <a href="msafree.html#M1">GeneratorSet</a> of <font color="Maroon">c<sub>5</sub></font> <b>by </b><i><a class="txt" href="equation.html#E2:25_1_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="equation.html#E3:25_1_1_1_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="msafree.html#T3">MSAFREE:3</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/><b>thus </b><a NAME="E7:25_1_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="pre_circ.html#V1">locally-finite</a>
 <b>by </b><i><a class="txt" href="equation.html#E2:25_1_1_1_1"><i><font color="Green">E13</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_1_1_1_2"><b>case </b></a><a NAME="E1:25_1_1_1_2"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="msualg_1.html#V2">void</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:25_1_1_1_2"/>
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> is <a href="pre_circ.html#V1">locally-finite</a>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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