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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>thus </b><a NAME="E1:1"/>
 <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="alg_1.html#R2">is_monomorphism</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="alg_1.html#D4">ALG_1:def 4</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:1_1"/>
 <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="alg_1.html#R1">is_homomorphism</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="alg_1.html#T6">ALG_1:6</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="alg_1.html#D2">ALG_1:def 2</a><br/>

<b>thus </b><a NAME="E2:1_1"/>
 <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:1"/>
 <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="alg_1.html#R3">is_epimorphism</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:1_2"/>
 <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="alg_1.html#R1">is_homomorphism</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="alg_1.html#T6">ALG_1:6</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="alg_1.html#D3">ALG_1:def 3</a><br/>

<b>thus </b><a NAME="E2:1_2"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>


</div><b>end;</b></div>


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