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<b>let </b><font color="Maroon" title="c3">f</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">f</font> is <a href="pcs_0.html#V16" title="PCS_0:attr.16">pcs-Str-yielding</a> implies ( <font color="Maroon" title="c3">f</font> is <a href="pcs_0.html#V7" title="PCS_0:attr.7">TolStr-yielding</a> &amp; <font color="Maroon" title="c3">f</font> is <a href="yellow_1.html#V1" title="YELLOW_1:attr.1">RelStr-yielding</a> ) )</span><br/>

<b>assume </b><a NAME="E1:98_1_1"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="pcs_0.html#V16" title="PCS_0:attr.16">pcs-Str-yielding</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">f</font> is <a href="pcs_0.html#V7" title="PCS_0:attr.7">TolStr-yielding</a> &amp; <font color="Maroon" title="c3">f</font> is <a href="yellow_1.html#V1" title="YELLOW_1:attr.1">RelStr-yielding</a> )</span><br/>

<b>thus </b><a NAME="E2:98_1_1"/>
<font color="Maroon" title="c3">f</font> is <a href="pcs_0.html#V7" title="PCS_0:attr.7">TolStr-yielding</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f</font> is <a href="yellow_1.html#V1" title="YELLOW_1:attr.1">RelStr-yielding</a></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">y</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#D13" target="_self" title="PCS_0:def.13">PCS_0:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">y</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">f</font> implies <font color="Maroon" title="c4">y</font> is    <a href="pcs_0.html#L1" title="PCS_0:struct.1">TolStr</a>  )</span><br/>

<b>thus </b><a NAME="E1:98_1_1_1"/>
( <font color="Maroon" title="c4">y</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">f</font> implies <font color="Maroon" title="c4">y</font> is    <a href="pcs_0.html#L1" title="PCS_0:struct.1">TolStr</a>  )
 <b>by </b><i><a class="txt" href="pcs_0.html#E1:98_1_1"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="pcs_0.html#D28" target="_self" title="PCS_0:def.28">Def28</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>let </b><font color="Maroon" title="c4">y</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="yellow_1.html#D3" title="YELLOW_1:def.3">YELLOW_1:def 3</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="c4">y</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">f</font> or <font color="Maroon" title="c4">y</font> is    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  )</span><br/>

<b>thus </b><a NAME="E3:98_1_1"/>
(  not <font color="Maroon" title="c4">y</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">f</font> or <font color="Maroon" title="c4">y</font> is    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  )
 <b>by </b><i><a class="txt" href="pcs_0.html#E1:98_1_1"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="pcs_0.html#D28" target="_self" title="PCS_0:def.28">Def28</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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