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<span class="kw">let </span><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="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">U1</font> being  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">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/><span class="kw">let </span><font color="Maroon" title="c2">U1</font> be   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E1:17"/>
( <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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="endalg.html#D4" target="_self" title="ENDALG:def.4">Def4</a></span>;<br/>
<a NAME="E2:17"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_3.html#T10" title="MSUALG_3:th.10">MSUALG_3:10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:17"/>
<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 class="kw">by</span> <span class="lab"><a class="ref" href="endalg.html#D4" target="_self" title="ENDALG:def.4">Def4</a></span>; <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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