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<b>let </b><font color="Maroon" title="c1">x1</font>, <font color="Maroon" title="c2">y1</font>, <font color="Maroon" title="c3">x2</font>, <font color="Maroon" title="c4">y2</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"> ( <font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c4">y2</font> iff ( <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> &amp; <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font> ) )</span><br/>

<a NAME="E1:139"/><i><font color="Green" title="E80">A1</font></i>: 
( <font color="Maroon" title="c3">x2</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c4">y2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font> iff ( <font color="Maroon" title="c3">x2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">x1</font> &amp; <font color="Maroon" title="c4">y2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">y1</font> ) )
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T79" target="_self" title="COHSP_1:th.79">Th79</a></i>;<br/>
<a NAME="E2:139"/>
( <font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">x2</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c4">y2</font> iff ( <font color="Maroon" title="c1">x1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">x2</font> &amp; <font color="Maroon" title="c2">y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">y2</font> ) )
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T79" target="_self" title="COHSP_1:th.79">Th79</a></i>;<br/>
<b>hence </b><a NAME="E3:139"/>
( <font color="Maroon" title="c1">x1</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> <a href="cohsp_1.html#K14" title="COHSP_1:func.14">U+</a> <font color="Maroon" title="c4">y2</font> iff ( <font color="Maroon" title="c1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> &amp; <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font> ) )
 <b>by </b><i><a class="txt" href="#E1:139"><i><font color="Green" title="E80">A1</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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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