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<span class="kw">let </span><font color="Maroon" title="c3">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">R</font> is  <a href="yellow16.html#V1" title="YELLOW16:attr.1">Poset-yielding</a>  implies <font color="Maroon" title="c3">R</font> is  <a href="pcs_0.html#V1" title="PCS_0:attr.1">transitive-yielding</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:18_1_1"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<font color="Maroon" title="c3">R</font> is  <a href="yellow16.html#V1" title="YELLOW16:attr.1">Poset-yielding</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">R</font> is  <a href="pcs_0.html#V1" title="PCS_0:attr.1">transitive-yielding</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">S</font> be    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="pcs_0.html#D4" target="_self" title="PCS_0:def.4">PCS_0:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c3">R</font> implies <font color="Maroon" title="c4">S</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:18_1_1"/>
( <font color="Maroon" title="c4">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c3">R</font> implies <font color="Maroon" title="c4">S</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_1"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="yellow16.html#D5" title="YELLOW16:def.5">YELLOW16:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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