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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font>, <font color="Maroon" title="c3">S3</font> be    <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/>

<b>given </b><font color="Maroon" title="c4">f1</font>, <font color="Maroon" title="c5">g1</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><a NAME="E2:64"/><i><font color="Green" title="E38">A1</font></i>: 
( <font color="Maroon" title="c4">f1</font>,<font color="Maroon" title="c5">g1</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c1">S1</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S1</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="pua2mss1.html#D14" target="_self" title="PUA2MSS1:def.14">PUA2MSS1:def 14</a><br/>

<b>given </b><font color="Maroon" title="c6">f2</font>, <font color="Maroon" title="c7">g2</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><a NAME="E4:64"/><i><font color="Green" title="E39">A2</font></i>: 
( <font color="Maroon" title="c6">f2</font>,<font color="Maroon" title="c7">g2</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c3">S3</font>,<font color="Maroon" title="c2">S2</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c2">S2</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="pua2mss1.html#D14" target="_self" title="PUA2MSS1:def.14">PUA2MSS1:def 14</a><br/>

<b>take </b><font color="Maroon" title="c8">f</font> = <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">f2</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="pua2mss1.html#D14" target="_self" title="PUA2MSS1:def.14">PUA2MSS1:def 14</a><br/>

<b>take </b><font color="Maroon" title="c9">g</font> = <font color="Maroon" title="c5">g1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">g2</font>;<br/>

<b>thus </b><a NAME="E5:64"/>
<font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c9">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c3">S3</font>,<font color="Maroon" title="c1">S1</font>
 <b>by </b><i><a class="txt" href="pua2mss1.html#E2:64"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="pua2mss1.html#E4:64"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="pua2mss1.html#T30" target="_self" title="PUA2MSS1:th.30">Th30</a></i>;<br/>

<a NAME="E6:64"/>
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 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="txt" href="pua2mss1.html#E2:64"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="pua2mss1.html#D13" target="_self" title="PUA2MSS1:def.13">Def13</a></i>;<br/>
<b>hence </b><a NAME="E7:64"/>
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c9">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S1</font> )
 <b>by </b><i><a class="txt" href="pua2mss1.html#E2:64"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="pua2mss1.html#E4:64"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="relat_1.html#T47" title="RELAT_1:th.47">RELAT_1:47</a></i>;<br/>


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