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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="partpr_2.html#NM1" title="PARTPR_2:NM.1">BinominativeFunction</a> of <font color="Maroon" title="c1">D</font> holds   <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Olive" title="b1">f</font></span>)</span> is   <a href="partpr_2.html#NM1" title="PARTPR_2:NM.1">BinominativeFunction</a> of <font color="Maroon" title="c1">D</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="partpr_2.html#NM1" title="PARTPR_2:NM.1">BinominativeFunction</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Maroon" title="c2">f</font></span>)</span> is   <a href="partpr_2.html#NM1" title="PARTPR_2:NM.1">BinominativeFunction</a> of <font color="Maroon" title="c1">D</font></span><br/>



<a NAME="E1:11"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">D</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c2">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">D</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" onmouseover="rs('relat_1/D19')" onmouseout="rh()">RELAT_1:def 19</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">X</font> =  <a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Maroon" title="c2">f</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">D</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T8" onmouseover="rs('xboole_1/T8')" onmouseout="rh()">XBOOLE_1:8</a></span>;<br/>
<a NAME="E3:11"/>
 <a href="partfun2.html#K1" title="PARTFUN2:func.1">id</a> <font color="Maroon" title="c3">X</font> is   <a href="partpr_2.html#NM1" title="PARTPR_2:NM.1">BinominativeFunction</a> of <font color="Maroon" title="c1">D</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E4:11"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <font color="Maroon" title="c2">f</font></span>)</span> is   <a href="partpr_2.html#NM1" title="PARTPR_2:NM.1">BinominativeFunction</a> of <font color="Maroon" title="c1">D</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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