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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="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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</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="b3">C</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b4">h1</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font>  st <font color="Olive" title="b4">h1</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font> holds <br/>for <font color="Olive" title="b5">h2</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font>  st <font color="Olive" title="b4">h1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b5">h2</font> holds <br/><font color="Olive" title="b5">h2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Maroon" title="c2">A</font><br/> for <font color="Olive" title="b2">h1</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c3">B</font>,<font color="Olive" title="b1">C</font>  st <font color="Olive" title="b2">h1</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">B</font>,<font color="Olive" title="b1">C</font> holds <br/>for <font color="Olive" title="b3">h2</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font>  st <font color="Olive" title="b2">h1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b3">h2</font> holds <br/><font color="Olive" title="b3">h2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font></span><br/><b>let </b><font color="Maroon" title="c4">C</font> be  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Maroon" title="c2">A</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">h1</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font>  st <font color="Olive" title="b1">h1</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font> holds <br/>for <font color="Olive" title="b2">h2</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font>  st <font color="Olive" title="b1">h1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b2">h2</font> holds <br/><font color="Olive" title="b2">h2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font></span><br/><b>let </b><font color="Maroon" title="c5">h1</font> be   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">h1</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font> implies for <font color="Olive" title="b1">h2</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font>  st <font color="Maroon" title="c5">h1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b1">h2</font> holds <br/><font color="Olive" title="b1">h2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font> )</span><br/>







<b>assume </b><a NAME="E1:22"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c5">h1</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</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">h2</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font>  st <font color="Maroon" title="c5">h1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b1">h2</font> holds <br/><font color="Olive" title="b1">h2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font></span><br/>

<b>let </b><font color="Maroon" title="c6">h2</font> be   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">h1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c6">h2</font> implies <font color="Maroon" title="c6">h2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font> )</span><br/>

<b>assume </b><a NAME="E2:22"/><i><font color="Green" title="E8">A2</font></i>: 
<font color="Maroon" title="c5">h1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c6">h2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">h2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font></span><br/>

<a NAME="E3:22"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">C</font> is    <a href="pboole.html#M4" title="PBOOLE:mode.4">ManySortedSubset</a> of the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D10" title="MSUALG_2:def.10">MSUALG_2:def 10</a></i>;<br/>
<a NAME="E4:22"/><b>then </b>
 <a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">C</font> is   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="extens_1.html#T9" title="EXTENS_1:th.9">EXTENS_1:9</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c7">G</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font><b> such that </b><br/><a NAME="E6:22"/><i><font color="Green" title="E9">A3</font></i>: 
<font color="Maroon" title="c7">G</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c4">C</font>
 ;<br/>
<a NAME="E7:22"/><i><font color="Green" title="E10">A4</font></i>: 
<font color="Maroon" title="c7">G</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Maroon" title="c5">h1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">h1</font>
 
<b>by </b><i><a class="txt" href="#E6:22"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="msualg_3.html#T4" title="MSUALG_3:th.4">MSUALG_3:4</a></i>;<br/>
<a NAME="E8:22"/>
<font color="Maroon" title="c7">G</font> <a href="msualg_3.html#R3" title="MSUALG_3:pred.3">is_monomorphism</a> <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E6:22"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="msualg_3.html#T22" title="MSUALG_3:th.22">MSUALG_3:22</a></i>;<br/>
<a NAME="E9:22"/><b>then </b>
<font color="Maroon" title="c7">G</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="msualg_3.html#D11" title="MSUALG_3:def.11">MSUALG_3:def 11</a></i>;<br/>
<b>hence </b><a NAME="E10:22"/>
<font color="Maroon" title="c6">h2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="#E1:22"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="#E2:22"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="#E7:22"><i><font color="Green" title="E10">A4</font></i></a>, <a class="ref" href="msualg_3.html#T10" title="MSUALG_3:th.10">MSUALG_3:10</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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