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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font>, <font color="Maroon" title="c3">S3</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</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">A1</font> being <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S1</font><br/> for <font color="Olive" title="b2">A2</font> being <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">S2</font><br/> for <font color="Olive" title="b3">A3</font> being   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c3">S3</font>  st <font color="Olive" title="b1">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b2">A2</font> &amp; <font color="Olive" title="b2">A2</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b3">A3</font> &amp; <font color="Olive" title="b3">A3</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b1">A1</font> holds <br/><font color="Olive" title="b1">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Olive" title="b2">A2</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b3">A3</font></span><br/><b>let </b><font color="Maroon" title="c4">A1</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</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"> for <font color="Olive" title="b1">A2</font> being <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">S2</font><br/> for <font color="Olive" title="b2">A3</font> being   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c3">S3</font>  st <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b1">A2</font> &amp; <font color="Olive" title="b1">A2</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b2">A3</font> &amp; <font color="Olive" title="b2">A3</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c4">A1</font> holds <br/><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Olive" title="b1">A2</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b2">A3</font></span><br/><b>let </b><font color="Maroon" title="c5">A2</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">S2</font>; <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">A3</font> being   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c3">S3</font>  st <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c5">A2</font> &amp; <font color="Maroon" title="c5">A2</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b1">A3</font> &amp; <font color="Olive" title="b1">A3</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c4">A1</font> holds <br/><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b1">A3</font></span><br/><b>let </b><font color="Maroon" title="c6">A3</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c3">S3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c5">A2</font> &amp; <font color="Maroon" title="c5">A2</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c6">A3</font> &amp; <font color="Maroon" title="c6">A3</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c4">A1</font> implies <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c6">A3</font> )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:37"/><i><font color="Green" title="E23">A1</font></i>: 
( <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c2">S2</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font> &amp; the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c4">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c5">A2</font> )
 <b>and </b><br/><a NAME="E2:37"/><i><font color="Green" title="E24">A2</font></i>: 
( <font color="Maroon" title="c2">S2</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c3">S3</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c6">A3</font> &amp; the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c5">A2</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c6">A3</font> )
 <b>and </b><br/><a NAME="E3:37"/><i><font color="Green" title="E25">A3</font></i>: 
( <font color="Maroon" title="c3">S3</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c1">S1</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c6">A3</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A1</font> &amp; the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c6">A3</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c4">A1</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D3" target="_self" title="CIRCCOMB:def.3">CIRCCOMB:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c6">A3</font></span><br/>

<b>thus </b><a NAME="E4:37"/>
<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c3">S3</font>
 <b>by </b><i><a class="txt" href="circcomb.html#E1:37"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="circcomb.html#E2:37"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="circcomb.html#E3:37"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="circcomb.html#T7" target="_self" title="CIRCCOMB:th.7">Th7</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D3" target="_self" title="CIRCCOMB:def.3">CIRCCOMB:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c6">A3</font> &amp; the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c6">A3</font> )</span><br/>

<a NAME="E5:37"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> <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="c4">A1</font> <a href="circcomb.html#K1" title="CIRCCOMB:func.1">+*</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A2</font>
 
<b>by </b><i><a class="txt" href="circcomb.html#E1:37"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="circcomb.html#D4" target="_self" title="CIRCCOMB:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E6:37"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c6">A3</font>
 <b>by </b><i><a class="txt" href="circcomb.html#E1:37"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="circcomb.html#E2:37"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="circcomb.html#E3:37"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="circcomb.html#T5" target="_self" title="CIRCCOMB:th.5">Th5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c6">A3</font></span><br/>

<a NAME="E7:37"/>
the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> <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="c4">A1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c5">A2</font>
 
<b>by </b><i><a class="txt" href="circcomb.html#E1:37"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="circcomb.html#D4" target="_self" title="CIRCCOMB:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E8:37"/>
the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c6">A3</font>
 <b>by </b><i><a class="txt" href="circcomb.html#E1:37"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="circcomb.html#E2:37"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="circcomb.html#E3:37"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="circcomb.html#T5" target="_self" title="CIRCCOMB:th.5">Th5</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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