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<a NAME="E1:99_1_1"/>
<font color="Maroon" title="c3">I</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c4">P</font> is <a href="pcs_0.html#V17" title="PCS_0:attr.17">pcs-yielding</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pcs_0.html#D33" target="_self" title="PCS_0:def.33">PCS_0:def 33</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">I</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c4">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> is   <a href="pcs_0.html#NM1" title="PCS_0:NM.1">pcs</a> )</span><br/>

<b>thus </b><a NAME="E1:99_1_1_1"/>
( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">I</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">I</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c4">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> is   <a href="pcs_0.html#NM1" title="PCS_0:NM.1">pcs</a> )
 <b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:99_1_1"/>
<font color="Maroon" title="c3">I</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c4">P</font> is  <a href="pcs_0.html#V17" title="PCS_0:attr.17">V209</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c3">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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