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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  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <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#V2" title="FUNCT_1:attr.2">one-to-one</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><a NAME="E2:50"/><i><font color="Green" title="E31">A1</font></i>: 
<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> <a href="circtrm1.html#R1" title="CIRCTRM1:pred.1">are_equivalent_wrt</a> <font color="Maroon" title="c4">f1</font>,<font color="Maroon" title="c5">g1</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circtrm1.html#D10" target="_self" title="CIRCTRM1:def.10">CIRCTRM1:def 10</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#V2" title="FUNCT_1:attr.2">one-to-one</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><a NAME="E4:50"/><i><font color="Green" title="E32">A2</font></i>: 
<font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">S3</font> <a href="circtrm1.html#R1" title="CIRCTRM1:pred.1">are_equivalent_wrt</a> <font color="Maroon" title="c6">f2</font>,<font color="Maroon" title="c7">g2</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circtrm1.html#D10" target="_self" title="CIRCTRM1:def.10">CIRCTRM1:def 10</a><br/>

<b>take </b>
<font color="Maroon" title="c6">f2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">f1</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="circtrm1.html#D10" target="_self" title="CIRCTRM1:def.10">CIRCTRM1:def 10</a><br/>

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

<b>thus </b><a NAME="E5:50"/>
<font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">S3</font> <a href="circtrm1.html#R1" title="CIRCTRM1:pred.1">are_equivalent_wrt</a> <font color="Maroon" title="c6">f2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">f1</font>,<font color="Maroon" title="c7">g2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">g1</font>
 <b>by </b><i><a class="txt" href="circtrm1.html#E2:50"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="circtrm1.html#E4:50"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="circtrm1.html#T28" target="_self" title="CIRCTRM1:th.28">Th28</a></i>;<br/>


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