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<b>let </b><font color="Maroon" title="c1">S1</font> be   <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">U1</font> being  <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Maroon" title="c1">S1</font> holds <br/> ( <font color="Olive" title="b1">U1</font> is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a> iff  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b1">U1</font> #) is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a> )</span><br/><b>let </b><font color="Maroon" title="c2">U1</font> be   <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Maroon" title="c1">S1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">U1</font> is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a> iff  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #) is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a> )</span><br/>



<b>set </b><font color="Maroon" title="c3">U2</font> =  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #);<br/>
<div><i><font color="Green" title="E16">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">o1</font> be   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #) &amp;  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #) )</span><br/><b>thus </b> <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font> = 
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #) <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c4">o1</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D11" title="MSUALG_1:def.11">MSUALG_1:def 11</a></i>
<br/>.= 
 <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)
<b>by </b><i><a class="ref" href="msualg_1.html#D11" title="MSUALG_1:def.11">MSUALG_1:def 11</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span><br/><b>thus </b> <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</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#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">o1</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D9" title="MSUALG_1:def.9">MSUALG_1:def 9</a></i>
<br/>.= 
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)
<b>by </b><i><a class="ref" href="msualg_1.html#D9" title="MSUALG_1:def.9">MSUALG_1:def 9</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>thus </b><a NAME="E2:25"/>
( <font color="Maroon" title="c2">U1</font> is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a> implies  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #) is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #) is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a> implies <font color="Maroon" title="c2">U1</font> is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:25_2"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c2">U1</font> is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #) is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a></span><br/>

<b>let </b><font color="Maroon" title="c4">o1</font>, <font color="Maroon" title="c5">o2</font> be   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S1</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D23" title="OSALG_1:def.23">OSALG_1:def 23</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">o1</font> <a href="osalg_1.html#R6" title="OSALG_1:pred.6">&lt;=</a> <font color="Maroon" title="c5">o2</font> or <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o2</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #) )</span><br/>

<b>assume </b><a NAME="E2:25_2"/><i><font color="Green" title="E18">A3</font></i>: 
<font color="Maroon" title="c4">o1</font> <a href="osalg_1.html#R6" title="OSALG_1:pred.6">&lt;=</a> <font color="Maroon" title="c5">o2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o2</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span><br/>

<a NAME="E3:25_2"/><i><font color="Green" title="E19">A4</font></i>: 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c2">U1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font>
 
<b>by </b><i><a class="txt" href="#E1:25_2"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="#E2:25_2"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="osalg_1.html#D23" title="OSALG_1:def.23">OSALG_1:def 23</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o2</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span>)</span> = 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c2">U1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span>)</span>
<b>by </b><i><a class="txt" href="#E1:25"><i><font color="Green" title="E16">A1</font></i></a></i>
<br/>.= 
 <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font>
<b>by </b><i><a class="txt" href="#E1:25"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E3:25_2"><i><font color="Green" title="E19">A4</font></i></a></i>
<br/>.= 
 <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)
<b>by </b><i><a class="txt" href="#E1:25"><i><font color="Green" title="E16">A1</font></i></a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:25"/><i><font color="Green" title="E17">A5</font></i>: 
 <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #) is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">U1</font> is <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</a></span><br/>

<b>let </b><font color="Maroon" title="c4">o1</font>, <font color="Maroon" title="c5">o2</font> be   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S1</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D23" title="OSALG_1:def.23">OSALG_1:def 23</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">o1</font> <a href="osalg_1.html#R6" title="OSALG_1:pred.6">&lt;=</a> <font color="Maroon" title="c5">o2</font> or <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c2">U1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font> )</span><br/>

<b>assume </b><a NAME="E4:25"/><i><font color="Green" title="E18">A6</font></i>: 
<font color="Maroon" title="c4">o1</font> <a href="osalg_1.html#R6" title="OSALG_1:pred.6">&lt;=</a> <font color="Maroon" title="c5">o2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c2">U1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font></span><br/>

<a NAME="E5:25"/><i><font color="Green" title="E19">A7</font></i>: 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o2</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)
 
<b>by </b><i><a class="txt" href="#E3:25"><i><font color="Green" title="E17">A5</font></i></a>, <a class="txt" href="#E4:25"><i><font color="Green" title="E18">A6</font></i></a>, <a class="ref" href="osalg_1.html#D23" title="OSALG_1:def.23">OSALG_1:def 23</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c2">U1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c5">o2</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)</span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:25"><i><font color="Green" title="E16">A1</font></i></a></i>
<br/>.= 
 <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U1</font> #)
<b>by </b><i><a class="txt" href="#E1:25"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E5:25"><i><font color="Green" title="E19">A7</font></i></a></i>
<br/>.= 
 <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c2">U1</font>
<b>by </b><i><a class="txt" href="#E1:25"><i><font color="Green" title="E16">A1</font></i></a></i>
; <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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