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<b>let </b><font color="Maroon" title="c2">a</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="orders_3.html#D4" title="ORDERS_3:def.4">ORDERS_3:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow21.html#K2" title="YELLOW21:func.2">POSETS</a> <font color="Maroon" title="c1">W</font> or <font color="Maroon" title="c2">a</font> is    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  )</span><br/>

<b>assume </b><a NAME="E1:4_1_1"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow21.html#K2" title="YELLOW21:func.2">POSETS</a> <font color="Maroon" title="c1">W</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> is    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> </span><br/>

<a NAME="E2:4_1_1"/><b>then </b><i><font color="Green" title="E4">A2</font></i>: 
( <font color="Maroon" title="c2">a</font> is  <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="yellow21.html#K1" title="YELLOW21:func.1">as_1-sorted</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font> )
 
<b>by </b><i><a class="ref" href="yellow21.html#D2" target="_self" title="YELLOW21:def.2">Def2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">a</font> = <font color="Maroon" title="c2">a</font> as   <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a> <b>by </b><i><a class="txt" href="yellow21.html#E1:4_1_1"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="yellow21.html#D2" target="_self" title="YELLOW21:def.2">Def2</a></i>;<br/>
<a NAME="E4:4_1_1"/>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="yellow21.html#K1" title="YELLOW21:func.1">as_1-sorted</a>  &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="yellow21.html#K1" title="YELLOW21:func.1">as_1-sorted</a> </span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="txt" href="yellow21.html#E2:4_1_1"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="yellow21.html#D1" target="_self" title="YELLOW21:def.1">Def1</a>, <a class="ref" href="setfam_1.html#D9" title="SETFAM_1:def.9">SETFAM_1:def 9</a></i>;<br/>
<b>hence </b><a NAME="E5:4_1_1"/>
<font color="Maroon" title="c2">a</font> is    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> 
 <b>by </b><i><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>; <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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