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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</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> ;<br/><b>let </b><font color="Maroon" title="c3">X</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font>;<br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font>;<br/><b>let </b><font color="Maroon" title="c5">g</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>







<b>assume </b><a NAME="E1:53"/><i><font color="Green" title="E30">A1</font></i>: 
<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c6">h</font> = <font color="Maroon" title="c5">g</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S1</font>,the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c2">S2</font> <b>by </b><i><a class="ref" href="instalg1.html#T10" target="_self" title="INSTALG1:th.10">Th10</a></i>;<br/>
<b>set </b><font color="Maroon" title="c7">F</font> =  <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font>;<br/>
<b>let </b><font color="Maroon" title="c8">o</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S1</font>;<br/><b>let </b><font color="Maroon" title="c9">p</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c8">o</font>,<span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span>;<br/><b>let </b><font color="Maroon" title="c10">q</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/>





<b>assume </b><a NAME="E3:53"/><i><font color="Green" title="E31">A2</font></i>: 
<font color="Maroon" title="c10">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c9">p</font>
 ;<br/>

<a NAME="E4:53"/><b>then </b><i><font color="Green" title="E32">A3</font></i>: 
<font color="Maroon" title="c10">q</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">o</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">X</font></span>)</span>
 
<b>by </b><i><a class="txt" href="instalg1.html#E1:53"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="instalg1.html#T25" target="_self" title="INSTALG1:th.25">Th25</a></i>;<br/>
<a NAME="E5:53"/>
 <a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>
 
<b>by </b><i><a class="txt" href="instalg1.html#E1:53"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="instalg1.html#D5" target="_self" title="INSTALG1:def.5">Def5</a></i>;<br/>
<a NAME="E6:53"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c8">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c8">o</font>,<span class="p3">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c8">o</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">q</font>
 
<b>by </b><i><a class="txt" href="instalg1.html#E3:53"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="msualg_3.html#D9" title="MSUALG_3:def.9">MSUALG_3:def 9</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="instalg1.html#K3" title="INSTALG1:func.3">hom</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c8">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">o</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c9">p</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c8">o</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">q</font>
<b>by </b><i><a class="ref" href="instalg1.html#T4" target="_self" title="INSTALG1:th.4">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">o</font></span>)</span>,<span class="p2">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c3">X</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">q</font>
<b>by </b><i><a class="txt" href="instalg1.html#E1:53"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="instalg1.html#T24" target="_self" title="INSTALG1:th.24">Th24</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">o</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c10">q</font>
<b>by </b><i><a class="txt" href="instalg1.html#E4:53"><i><font color="Green" title="E32">A3</font></i></a>, <a class="ref" href="instalg1.html#T4" target="_self" title="INSTALG1:th.4">Th4</a></i>
;<br/><br/>


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