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<b>let </b><font color="Maroon">S1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> , <font color="Maroon">S2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> , <font color="Maroon">S3</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/>

<b>given </b><font color="Maroon">f1</font> being  <a href="funct_1.html#V2">one-to-one</a> <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g1</font> being  <a href="funct_1.html#V2">one-to-one</a> <a href="funct_1.html#NM1">Function</a><b> such that </b><a NAME="E1:52"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">S1</font>,<font color="Maroon">S2</font> <a href="circtrm1.html#R1" target="_self">are_equivalent_wrt</a> <font color="Maroon">f1</font>,<font color="Maroon">g1</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circtrm1.html#D10" target="_self">CIRCTRM1:def 10</a><br/>

<b>given </b><font color="Maroon">f2</font> being  <a href="funct_1.html#V2">one-to-one</a> <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g2</font> being  <a href="funct_1.html#V2">one-to-one</a> <a href="funct_1.html#NM1">Function</a><b> such that </b><a NAME="E2:52"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">S2</font>,<font color="Maroon">S3</font> <a href="circtrm1.html#R1" target="_self">are_equivalent_wrt</a> <font color="Maroon">f2</font>,<font color="Maroon">g2</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circtrm1.html#D10" target="_self">CIRCTRM1:def 10</a><br/>

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

<b>take </b>
<font color="Maroon">g2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g1</font>
;<br/>

<b>thus </b><a NAME="E3:52"/>
<font color="Maroon">S1</font>,<font color="Maroon">S3</font> <a href="circtrm1.html#R1" target="_self">are_equivalent_wrt</a> <font color="Maroon">f2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f1</font>,<font color="Maroon">g2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g1</font>
 <b>by </b><i>, , </i>;<br/>


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