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<span class="kw">let </span><font color="Maroon" title="c1">UA</font> be   <a href="unialg_1.html#NM1" title="UNIALG_1:NM.1">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">UA</font> <a href="alg_1.html#R4" title="ALG_1:pred.4">is_isomorphism</a> <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">I</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">UA</font>;<br/>
<a NAME="E1:1"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">UA</font> <a href="alg_1.html#R1" title="ALG_1:pred.1">is_homomorphism</a> <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="alg_1.html#T5" title="ALG_1:th.5">ALG_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:1"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">UA</font> <a href="alg_1.html#R2" title="ALG_1:pred.2">is_monomorphism</a> <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="alg_1.html#D2" title="ALG_1:def.2">ALG_1:def 2</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="alg_1.html#D4" title="ALG_1:def.4">ALG_1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">UA</font> <a href="alg_1.html#R3" title="ALG_1:pred.3">is_epimorphism</a> <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font></span><br/>

<a NAME="E3:1"/>
(  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">UA</font> <a href="alg_1.html#R1" title="ALG_1:pred.1">is_homomorphism</a> <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">UA</font></span>)</span> <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">UA</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="alg_1.html#T5" title="ALG_1:th.5">ALG_1:5</a>, <a class="ref" href="relat_1.html#T45" title="RELAT_1:th.45">RELAT_1:45</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:1"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">UA</font> <a href="alg_1.html#R3" title="ALG_1:pred.3">is_epimorphism</a> <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="alg_1.html#D3" title="ALG_1:def.3">ALG_1:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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