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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font><br/>  for <font color="Olive" title="b2">A</font> being   <a href="pralg_1.html#V2" title="PRALG_1:attr.2">1-sorted-yielding</a>   <a href="pencil_1.html#V14" title="PENCIL_1:attr.14">non-Trivial-yielding</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  holds  not <font color="Olive" title="b2">A</font> <a href="pralg_1.html#K10" title="PRALG_1:func.10">.</a> <font color="Olive" title="b1">i</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being   <a href="pralg_1.html#V2" title="PRALG_1:attr.2">1-sorted-yielding</a>   <a href="pencil_1.html#V14" title="PENCIL_1:attr.14">non-Trivial-yielding</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  holds  not <font color="Olive" title="b1">A</font> <a href="pralg_1.html#K10" title="PRALG_1:func.10">.</a> <font color="Maroon" title="c2">i</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="pralg_1.html#V2" title="PRALG_1:attr.2">1-sorted-yielding</a>   <a href="pencil_1.html#V14" title="PENCIL_1:attr.14">non-Trivial-yielding</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c3">A</font> <a href="pralg_1.html#K10" title="PRALG_1:func.10">.</a> <font color="Maroon" title="c2">i</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> </span><br/>





<a NAME="E1:2"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E2:2"/><span class="kw">then </span>
<font color="Maroon" title="c3">A</font> <a href="pralg_1.html#K10" title="PRALG_1:func.10">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T3" title="FUNCT_1:th.3">FUNCT_1:3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:2"/>
 not <font color="Maroon" title="c3">A</font> <a href="pralg_1.html#K10" title="PRALG_1:func.10">.</a> <font color="Maroon" title="c2">i</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pencil_1.html#D17" title="PENCIL_1:def.17">PENCIL_1:def 17</a></span>; <a class="txt" 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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