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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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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> over <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#R8" title="PBOOLE:pred.8">=</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/><span class="kw">let </span><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> over <font color="Maroon" title="c1">S</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#R8" title="PBOOLE:pred.8">=</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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#R8" title="PBOOLE:pred.8">=</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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#R8" title="PBOOLE:pred.8">=</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/>







<span class="kw">assume </span><a NAME="E1:22"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#R8" title="PBOOLE:pred.8">=</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/>

<a NAME="E2:22"/>
 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#M3" title="PBOOLE:mode.3">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" onmouseover="rs('msualg_2/D9')" onmouseout="rh()">MSUALG_2:def 9</a></span>;<br/>
<a NAME="E3:22"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extens_1.html#T5" onmouseover="rs('extens_1/T5')" onmouseout="rh()">EXTENS_1:5</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">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><span class="kw"> such that </span><br/><a NAME="E5:22"/><span class="lab"><font color="Green" title="E8">A2</font></span>: 
<font color="Maroon" title="c6">G</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</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="E6:22"/>
<font color="Maroon" title="c6">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="msualg_3.html#T22" onmouseover="rs('msualg_3/T22')" onmouseout="rh()">MSUALG_3:22</a></span>;<br/>
<a NAME="E7:22"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A3</font></span>: 
<font color="Maroon" title="c6">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>
 
;<br/>
<a NAME="E8:22"/><span class="lab"><font color="Green" title="E10">A4</font></span>: 
<font color="Maroon" title="c6">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#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c5">h1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="msualg_3.html#T4" onmouseover="rs('msualg_3/T4')" onmouseout="rh()">MSUALG_3:4</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">h1</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c7">h2</font> implies <font color="Maroon" title="c7">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/>

<span class="kw">assume </span><a NAME="E9:22"/>
<font color="Maroon" title="c5">h1</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c7">h2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">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/>

<span class="kw">hence </span><a NAME="E10:22"/>
<font color="Maroon" title="c7">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="txt" href="#E8:22"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E7:22"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="ref" href="msualg_3.html#T10" onmouseover="rs('msualg_3/T10')" onmouseout="rh()">MSUALG_3:10</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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