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<span class="kw">set </span><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/>
<span class="kw">set </span><font color="Maroon" title="c4">s0</font> = the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">M</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">c0</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">M</font>;<br/>
<a NAME="E1:67_1_1"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#D6" target="_self" title="OSALG_1:def.6">Def6</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">s1</font> = the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">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> ;<br/>
<a NAME="E3:67_1_1"/>
( the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">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#U1" title="MSUALG_1:sel.1">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#U2" title="MSUALG_1:sel.2">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#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S0</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#D6" target="_self" title="OSALG_1:def.6">Def6</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">c1</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">M</font> as    <a href="pboole.html#M2" title="PBOOLE:mode.2">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="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">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="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="osalg_1.html#D6" target="_self" title="OSALG_1:def.6">Def6</a></span>;<br/>
<a NAME="E5:67_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/>
<span class="kw">hence </span><a NAME="E6:67_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">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#U3" title="MSUALG_1:sel.3">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#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">M</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">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#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">M</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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