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<b>set </b><font color="Maroon" title="c3">S1</font> =  <a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font>;<br/>
<b>set </b><font color="Maroon" title="c4">s0</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">M</font>;<br/>
<b>set </b><font color="Maroon" title="c5">c0</font> = the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c2">M</font>;<br/>
<a NAME="E1:67_1_1"/><i><font color="Green" title="E38">A1</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">S0</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span> &amp; the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">S0</font> )
 
<b>by </b><i><a class="ref" href="osalg_1.html#D6" target="_self" title="OSALG_1:def.6">Def6</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">s1</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">M</font> as   <a href="struct_0.html#NM8" title="STRUCT_0:NM.8">ManySortedSet</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span> <b>by </b><i><a class="ref" href="osalg_1.html#D6" target="_self" title="OSALG_1:def.6">Def6</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">c1</font> = the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c2">M</font> as    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">s1</font> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span>,<font color="Maroon" title="c6">s1</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span> <b>by </b><i><a class="txt" href="osalg_1.html#E1:67_1_1"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="osalg_1.html#D6" target="_self" title="OSALG_1:def.6">Def6</a></i>;<br/>
<a NAME="E4:67_1_1"/>
 <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c7">c1</font> #) is <a href="osalg_1.html#V12" title="OSALG_1:attr.12">order-sorted</a>
 
;<br/>
<b>hence </b><a NAME="E5:67_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">strict</a> <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of  <a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font> st <br/>( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">M</font> &amp; the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c2">M</font> )
 ; <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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