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<b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">X1</font>, <font color="Maroon" title="c4">X2</font>, <font color="Maroon" title="c5">X3</font>, <font color="Maroon" title="c6">X4</font>, <font color="Maroon" title="c7">X5</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Y</font>, <font color="Olive" title="b2">Y1</font>, <font color="Olive" title="b3">Y2</font>, <font color="Olive" title="b4">Y3</font>, <font color="Olive" title="b5">Y4</font>, <font color="Olive" title="b6">Y5</font> being <a href="valued_2.html#V1" title="VALUED_2:attr.1">complex-functions-membered</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b7">f</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c2">X</font>,<font color="Olive" title="b1">Y</font><br/> for <font color="Olive" title="b8">f1</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c3">X1</font>,<font color="Olive" title="b2">Y1</font><br/> for <font color="Olive" title="b9">f2</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c4">X2</font>,<font color="Olive" title="b3">Y2</font><br/> for <font color="Olive" title="b10">f3</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c5">X3</font>,<font color="Olive" title="b4">Y3</font><br/> for <font color="Olive" title="b11">f4</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c6">X4</font>,<font color="Olive" title="b5">Y4</font><br/> for <font color="Olive" title="b12">f5</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c7">X5</font>,<font color="Olive" title="b6">Y5</font>  st <font color="Olive" title="b10">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b8">f1</font> &amp; <font color="Olive" title="b11">f4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b9">f2</font> &amp; <font color="Olive" title="b12">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">f1</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Olive" title="b9">f2</font> holds <br/><font color="Olive" title="b7">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b12">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b10">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Olive" title="b11">f4</font></span><br/><b>let </b><font color="Maroon" title="c8">Y</font>, <font color="Maroon" title="c9">Y1</font>, <font color="Maroon" title="c10">Y2</font>, <font color="Maroon" title="c11">Y3</font>, <font color="Maroon" title="c12">Y4</font>, <font color="Maroon" title="c13">Y5</font> be  <a href="valued_2.html#V1" title="VALUED_2:attr.1">complex-functions-membered</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c8">Y</font><br/> for <font color="Olive" title="b2">f1</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c3">X1</font>,<font color="Maroon" title="c9">Y1</font><br/> for <font color="Olive" title="b3">f2</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c4">X2</font>,<font color="Maroon" title="c10">Y2</font><br/> for <font color="Olive" title="b4">f3</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c11">Y3</font><br/> for <font color="Olive" title="b5">f4</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c6">X4</font>,<font color="Maroon" title="c12">Y4</font><br/> for <font color="Olive" title="b6">f5</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c7">X5</font>,<font color="Maroon" title="c13">Y5</font>  st <font color="Olive" title="b4">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b2">f1</font> &amp; <font color="Olive" title="b5">f4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b3">f2</font> &amp; <font color="Olive" title="b6">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f1</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Olive" title="b3">f2</font> holds <br/><font color="Olive" title="b1">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b6">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Olive" title="b5">f4</font></span><br/><b>let </b><font color="Maroon" title="c14">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c8">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f1</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c3">X1</font>,<font color="Maroon" title="c9">Y1</font><br/> for <font color="Olive" title="b2">f2</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c4">X2</font>,<font color="Maroon" title="c10">Y2</font><br/> for <font color="Olive" title="b3">f3</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c11">Y3</font><br/> for <font color="Olive" title="b4">f4</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c6">X4</font>,<font color="Maroon" title="c12">Y4</font><br/> for <font color="Olive" title="b5">f5</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c7">X5</font>,<font color="Maroon" title="c13">Y5</font>  st <font color="Olive" title="b3">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b1">f1</font> &amp; <font color="Olive" title="b4">f4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b2">f2</font> &amp; <font color="Olive" title="b5">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f1</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Olive" title="b2">f2</font> holds <br/><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b5">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Olive" title="b4">f4</font></span><br/><b>let </b><font color="Maroon" title="c15">f1</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c3">X1</font>,<font color="Maroon" title="c9">Y1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f2</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c4">X2</font>,<font color="Maroon" title="c10">Y2</font><br/> for <font color="Olive" title="b2">f3</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c11">Y3</font><br/> for <font color="Olive" title="b3">f4</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c6">X4</font>,<font color="Maroon" title="c12">Y4</font><br/> for <font color="Olive" title="b4">f5</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c7">X5</font>,<font color="Maroon" title="c13">Y5</font>  st <font color="Olive" title="b2">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c15">f1</font> &amp; <font color="Olive" title="b3">f4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b1">f2</font> &amp; <font color="Olive" title="b4">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">f1</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Olive" title="b1">f2</font> holds <br/><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b4">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Olive" title="b3">f4</font></span><br/><b>let </b><font color="Maroon" title="c16">f2</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c4">X2</font>,<font color="Maroon" title="c10">Y2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f3</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c11">Y3</font><br/> for <font color="Olive" title="b2">f4</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c6">X4</font>,<font color="Maroon" title="c12">Y4</font><br/> for <font color="Olive" title="b3">f5</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c7">X5</font>,<font color="Maroon" title="c13">Y5</font>  st <font color="Olive" title="b1">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c15">f1</font> &amp; <font color="Olive" title="b2">f4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c16">f2</font> &amp; <font color="Olive" title="b3">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">f1</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c16">f2</font> holds <br/><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b3">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Olive" title="b2">f4</font></span><br/><b>let </b><font color="Maroon" title="c17">f3</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c11">Y3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f4</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c6">X4</font>,<font color="Maroon" title="c12">Y4</font><br/> for <font color="Olive" title="b2">f5</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c7">X5</font>,<font color="Maroon" title="c13">Y5</font>  st <font color="Maroon" title="c17">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c15">f1</font> &amp; <font color="Olive" title="b1">f4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c16">f2</font> &amp; <font color="Olive" title="b2">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">f1</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c16">f2</font> holds <br/><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b2">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Olive" title="b1">f4</font></span><br/><b>let </b><font color="Maroon" title="c18">f4</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c6">X4</font>,<font color="Maroon" title="c12">Y4</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f5</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c7">X5</font>,<font color="Maroon" title="c13">Y5</font>  st <font color="Maroon" title="c17">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c15">f1</font> &amp; <font color="Maroon" title="c18">f4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c16">f2</font> &amp; <font color="Olive" title="b1">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">f1</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c16">f2</font> holds <br/><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Olive" title="b1">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c18">f4</font></span><br/><b>let </b><font color="Maroon" title="c19">f5</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c7">X5</font>,<font color="Maroon" title="c13">Y5</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c17">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c15">f1</font> &amp; <font color="Maroon" title="c18">f4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c16">f2</font> &amp; <font color="Maroon" title="c19">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">f1</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c16">f2</font> implies <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c19">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c18">f4</font> )</span><br/>



































<b>assume </b><b>that </b><br/><a NAME="E1:244"/><i><font color="Green" title="E73">A1</font></i>: 
<font color="Maroon" title="c17">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c15">f1</font>
 <b>and </b><br/><a NAME="E2:244"/><i><font color="Green" title="E74">A2</font></i>: 
<font color="Maroon" title="c18">f4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c16">f2</font>
 <b>and </b><br/><a NAME="E3:244"/><i><font color="Green" title="E75">A3</font></i>: 
<font color="Maroon" title="c19">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">f1</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c16">f2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c19">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c18">f4</font></span><br/>

<a NAME="E4:244"/><i><font color="Green" title="E76">A4</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c17">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c14">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c15">f1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:244"><i><font color="Green" title="E73">A1</font></i></a>, <a class="ref" href="valued_2.html#D46" target="_self" title="VALUED_2:def.46">Def46</a></i>;<br/>
<a NAME="E5:244"/><i><font color="Green" title="E77">A5</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c18">f4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c14">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c16">f2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:244"><i><font color="Green" title="E74">A2</font></i></a>, <a class="ref" href="valued_2.html#D46" target="_self" title="VALUED_2:def.46">Def46</a></i>;<br/>
<a NAME="E6:244"/><i><font color="Green" title="E78">A6</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c19">f5</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c14">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c19">f5</font></span>)</span>
 
<b>by </b><i><a class="ref" href="valued_2.html#D46" target="_self" title="VALUED_2:def.46">Def46</a></i>;<br/>
<a NAME="E7:244"/><i><font color="Green" title="E79">A7</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c18">f4</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c17">f3</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c18">f4</font></span>)</span>
 
<b>by </b><i><a class="ref" href="valued_2.html#D45" target="_self" title="VALUED_2:def.45">Def45</a></i>;<br/>
<a NAME="E8:244"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c19">f5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c15">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c16">f2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E3:244"><i><font color="Green" title="E75">A3</font></i></a>, <a class="ref" href="valued_2.html#D45" target="_self" title="VALUED_2:def.45">Def45</a></i>;<br/>
<b>hence </b><a NAME="E9:244"/><i><font color="Green" title="E80">A8</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c19">f5</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c18">f4</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E7:244"><i><font color="Green" title="E79">A7</font></i></a>, <a class="txt" href="#E4:244"><i><font color="Green" title="E76">A4</font></i></a>, <a class="txt" href="#E5:244"><i><font color="Green" title="E77">A5</font></i></a>, <a class="txt" href="#E6:244"><i><font color="Green" title="E78">A6</font></i></a>, <a class="ref" href="valued_2.html#T1" target="_self" title="VALUED_2:th.1">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D17" title="FUNCT_1:def.17">FUNCT_1:def 17</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c19">f5</font></span>)</span> or <span class="p1">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c19">f5</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c18">f4</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/>

<b>let </b><font color="Maroon" title="c20">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="c20">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c19">f5</font></span>)</span> or <span class="p1">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c19">f5</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c18">f4</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font> )</span><br/>

<b>assume </b><a NAME="E10:244"/><i><font color="Green" title="E81">A9</font></i>: 
<font color="Maroon" title="c20">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c19">f5</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c19">f5</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c18">f4</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span><br/>

<a NAME="E11:244"/><b>then </b><i><font color="Green" title="E82">A10</font></i>: 
<font color="Maroon" title="c20">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c17">f3</font>
 
<b>by </b><i><a class="txt" href="#E7:244"><i><font color="Green" title="E79">A7</font></i></a>, <a class="txt" href="#E9:244"><i><font color="Green" title="E80">A8</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E12:244"/><i><font color="Green" title="E83">A11</font></i>: 
<font color="Maroon" title="c20">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c18">f4</font>
 
<b>by </b><i><a class="txt" href="#E7:244"><i><font color="Green" title="E79">A7</font></i></a>, <a class="txt" href="#E10:244"><i><font color="Green" title="E81">A9</font></i></a>, <a class="txt" href="#E9:244"><i><font color="Green" title="E80">A8</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E13:244"/><i><font color="Green" title="E84">A12</font></i>: 
<font color="Maroon" title="c20">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c19">f5</font>
 
<b>by </b><i><a class="txt" href="#E6:244"><i><font color="Green" title="E78">A6</font></i></a>, <a class="txt" href="#E10:244"><i><font color="Green" title="E81">A9</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="valued_2.html#K28" title="VALUED_2:func.28">&lt;##&gt;</a> <font color="Maroon" title="c19">f5</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">f5</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span>
<b>by </b><i><a class="txt" href="#E10:244"><i><font color="Green" title="E81">A9</font></i></a>, <a class="ref" href="valued_2.html#D46" target="_self" title="VALUED_2:def.46">Def46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:244"><i><font color="Green" title="E75">A3</font></i></a>, <a class="txt" href="#E13:244"><i><font color="Green" title="E84">A12</font></i></a>, <a class="ref" href="valued_2.html#D45" target="_self" title="VALUED_2:def.45">Def45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T27" title="RFUNCT_1:th.27">RFUNCT_1:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:244"><i><font color="Green" title="E73">A1</font></i></a>, <a class="txt" href="#E11:244"><i><font color="Green" title="E82">A10</font></i></a>, <a class="ref" href="valued_2.html#D46" target="_self" title="VALUED_2:def.46">Def46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">f3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">f4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font></span>)</span>
<b>by </b><i><a class="txt" href="#E12:244"><i><font color="Green" title="E83">A11</font></i></a>, <a class="txt" href="#E2:244"><i><font color="Green" title="E74">A2</font></i></a>, <a class="ref" href="valued_2.html#D46" target="_self" title="VALUED_2:def.46">Def46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">f3</font> <a href="valued_2.html#K27" title="VALUED_2:func.27">&lt;--&gt;</a> <font color="Maroon" title="c18">f4</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font>
<b>by </b><i><a class="txt" href="#E10:244"><i><font color="Green" title="E81">A9</font></i></a>, <a class="txt" href="#E9:244"><i><font color="Green" title="E80">A8</font></i></a>, <a class="ref" href="valued_2.html#D45" target="_self" title="VALUED_2:def.45">Def45</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>
