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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:59_1_1_1"/><i><font color="Green" title="E42">A1</font></i>: 
<font color="Maroon" title="c4">v</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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="pre_circ.html#K3" title="PRE_CIRC:func.3">|</a> <font color="Maroon" title="c3">Y</font></span>)</span>
 ;<br/><b>consider </b><font color="Maroon" title="c5">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:59_1_1_1"/><i><font color="Green" title="E43">A2</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="pre_circ.html#K3" title="PRE_CIRC:func.3">|</a> <font color="Maroon" title="c3">Y</font></span>)</span>
 <b>and </b><br/><a NAME="E4:59_1_1_1"/><i><font color="Green" title="E44">A3</font></i>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="pre_circ.html#K3" title="PRE_CIRC:func.3">|</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="txt" href="dickson.html#E1:59_1_1_1"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E5:59_1_1_1"/><i><font color="Green" title="E45">A4</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Y</font>
 <b>by </b><i><a class="txt" href="dickson.html#E3:59_1_1_1"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/><a NAME="E6:59_1_1_1"/><b>then </b><i><font color="Green" title="E46">A5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="pre_circ.html#K3" title="PRE_CIRC:func.3">|</a> <font color="Maroon" title="c3">Y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/><a NAME="E7:59_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="dickson.html#E5:59_1_1_1"><i><font color="Green" title="E45">A4</font></i></a></i>;<br/><a NAME="E8:59_1_1_1"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/><a NAME="E9:59_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</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="c2">p</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></i>;<br/><b>hence </b><a NAME="E10:59_1_1_1"/>
<font color="Maroon" title="c4">v</font> is    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> 
 <b>by </b><i><a class="txt" href="dickson.html#E4:59_1_1_1"><i><font color="Green" title="E44">A3</font></i></a>, <a class="txt" href="dickson.html#E6:59_1_1_1"><i><font color="Green" title="E46">A5</font></i></a>, <a class="ref" href="yellow_1.html#D3" title="YELLOW_1:def.3">YELLOW_1:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:59_1_1"/>
<font color="Maroon" title="c2">p</font> <a href="pre_circ.html#K3" title="PRE_CIRC:func.3">|</a> <font color="Maroon" title="c3">Y</font> is <a href="yellow_1.html#V1" title="YELLOW_1:attr.1">RelStr-yielding</a>
 <b>by </b><i><a class="ref" href="yellow_1.html#D3" title="YELLOW_1:def.3">YELLOW_1:def 3</a></i>;<br/>


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