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<b>let </b><font color="Maroon" title="c1">U1</font>, <font color="Maroon" title="c2">U2</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font>  st <font color="Olive" title="b1">f</font> <a href="alg_1.html#R3" title="ALG_1:pred.3">is_epimorphism</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> holds <br/> <a href="alg_1.html#K5" title="ALG_1:func.5">QuotUnivAlg</a> <font color="Maroon" title="c1">U1</font>,<span class="p1">(<span class="default"><a href="alg_1.html#K7" title="ALG_1:func.7">Cng</a> <font color="Olive" title="b1">f</font></span>)</span>,<font color="Maroon" title="c2">U2</font> <a href="alg_1.html#R5" title="ALG_1:pred.5">are_isomorphic</a> </span><br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">f</font> <a href="alg_1.html#R3" title="ALG_1:pred.3">is_epimorphism</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> implies  <a href="alg_1.html#K5" title="ALG_1:func.5">QuotUnivAlg</a> <font color="Maroon" title="c1">U1</font>,<span class="p1">(<span class="default"><a href="alg_1.html#K7" title="ALG_1:func.7">Cng</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">U2</font> <a href="alg_1.html#R5" title="ALG_1:pred.5">are_isomorphic</a>  )</span><br/>





<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E32">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="alg_1.html#R3" title="ALG_1:pred.3">is_epimorphism</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="alg_1.html#K5" title="ALG_1:func.5">QuotUnivAlg</a> <font color="Maroon" title="c1">U1</font>,<span class="p1">(<span class="default"><a href="alg_1.html#K7" title="ALG_1:func.7">Cng</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">U2</font> <a href="alg_1.html#R5" title="ALG_1:pred.5">are_isomorphic</a> </span><br/>

<b>take </b>
 <a href="alg_1.html#K8" title="ALG_1:func.8">HomQuot</a> <font color="Maroon" title="c3">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="alg_1.html#D5" target="_self" title="ALG_1:def.5">ALG_1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="alg_1.html#K8" title="ALG_1:func.8">HomQuot</a> <font color="Maroon" title="c3">f</font> <a href="alg_1.html#R4" title="ALG_1:pred.4">is_isomorphism</a>  <a href="alg_1.html#K5" title="ALG_1:func.5">QuotUnivAlg</a> <font color="Maroon" title="c1">U1</font>,<span class="p1">(<span class="default"><a href="alg_1.html#K7" title="ALG_1:func.7">Cng</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">U2</font></span><br/>

<b>thus </b><a NAME="E2:39"/>
 <a href="alg_1.html#K8" title="ALG_1:func.8">HomQuot</a> <font color="Maroon" title="c3">f</font> <a href="alg_1.html#R4" title="ALG_1:pred.4">is_isomorphism</a>  <a href="alg_1.html#K5" title="ALG_1:func.5">QuotUnivAlg</a> <font color="Maroon" title="c1">U1</font>,<span class="p1">(<span class="default"><a href="alg_1.html#K7" title="ALG_1:func.7">Cng</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c2">U2</font>
 <b>by </b><i><a class="txt" href="alg_1.html#E1:39"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="alg_1.html#T24" target="_self" title="ALG_1:th.24">Th24</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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