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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:17"/>
<font color="Maroon">c<sub>3</sub></font> <a href="yellow16.html#R1" target="_self">is_a_retraction_of</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:17"/><b>then </b><i><font color="Green">E15</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="yellow16.html#D1" target="_self">Def1</a>, <a class="ref" href="yellow16.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E3:17"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>
<b>hence </b><a NAME="E4:17"/>
 <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #)
 <b>by </b><i><a class="txt" href="yellow16.html#E2:17"><i><font color="Green">E15</font></i></a>, <a class="ref" href="yellow_0.html#T58">YELLOW_0:58</a></i>;<br/>


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