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<span class="kw">assume </span><a NAME="E1:2"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> is  <a href="abian.html#V2" title="ABIAN:attr.2">with_fixpoint</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"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:2"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
<font color="Maroon" title="c1">y</font> <a href="abian.html#R1" title="ABIAN:pred.1">is_a_fixpoint_of</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abian.html#D5" onmouseover="rs('abian/D5')" onmouseout="rh()">ABIAN:def 5</a></span>;<br/>
<a NAME="E4:2"/>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:2"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="ref" href="abian.html#D3" onmouseover="rs('abian/D3')" onmouseout="rh()">ABIAN:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:2"/>
contradiction
 ; <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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