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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> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">C1</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S1</font>;<br/><b>let </b><font color="Maroon">C2</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S2</font>;<br/>







<b>assume </b><a NAME="E1:62"/>
( <font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">g</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">S1</font>,<font color="Maroon">S2</font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">C2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font> &amp; the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">C2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g</font> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K2">"</a>  is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">g</font> <a href="funct_1.html#K2">"</a>  is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K2">"</a> ,<font color="Maroon">g</font> <a href="funct_1.html#K2">"</a>  <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">S2</font>,<font color="Maroon">S1</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circtrm1.html#D12" target="_self">CIRCTRM1:def 12</a>,<a class="ref" href="circtrm1.html#D13" target="_self">CIRCTRM1:def 13</a><br/>

<b>hence </b><a NAME="E2:62"/>
(  not the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">C2</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">C1</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K2">"</a> </span>)</span> or  not the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">C2</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">C1</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K2">"</a> </span>)</span> or <font color="Maroon">S1</font>,<font color="Maroon">S2</font> <a href="circtrm1.html#R1" target="_self">are_equivalent_wrt</a> <font color="Maroon">f</font>,<font color="Maroon">g</font> )
 <b>by </b><i/>;<br/>


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