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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</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">U1</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">S</font><br/> for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being   <a href="autalg_1.html#M2" title="AUTALG_1:mode.2">Element</a> of  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <font color="Olive" title="b1">U1</font> holds  <font color="Olive" title="b2">f1</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Olive" title="b3">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <font color="Olive" title="b1">U1</font></span><br/><b>let </b><font color="Maroon" title="c2">U1</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">S</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">f1</font>, <font color="Olive" title="b2">f2</font> being   <a href="autalg_1.html#M2" title="AUTALG_1:mode.2">Element</a> of  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <font color="Maroon" title="c2">U1</font> holds  <font color="Olive" title="b1">f1</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Olive" title="b2">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <font color="Maroon" title="c2">U1</font></span><br/><b>let </b><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be    <a href="autalg_1.html#M2" title="AUTALG_1:mode.2">Element</a> of  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <font color="Maroon" title="c2">U1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f1</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Maroon" title="c4">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <font color="Maroon" title="c2">U1</font></span><br/>





<a NAME="E1:14"/>
( <font color="Maroon" title="c3">f1</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c2">U1</font>,<font color="Maroon" title="c2">U1</font> &amp; <font color="Maroon" title="c4">f2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c2">U1</font>,<font color="Maroon" title="c2">U1</font> )
 
<b>by </b><i><a class="ref" href="endalg.html#D4" target="_self" title="ENDALG:def.4">Def4</a></i>;<br/>
<a NAME="E2:14"/><b>then </b>
<font color="Maroon" title="c3">f1</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Maroon" title="c4">f2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c2">U1</font>,<font color="Maroon" title="c2">U1</font>
 
<b>by </b><i><a class="ref" href="msualg_3.html#T10" title="MSUALG_3:th.10">MSUALG_3:10</a></i>;<br/>
<b>hence </b><a NAME="E3:14"/>
<font color="Maroon" title="c3">f1</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Maroon" title="c4">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="endalg.html#K4" title="ENDALG:func.4">MSAEnd</a> <font color="Maroon" title="c2">U1</font>
 <b>by </b><i><a class="ref" href="endalg.html#D4" target="_self" title="ENDALG:def.4">Def4</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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