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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E1:140"/><span class="lab"><font color="Green" title="E80">A1</font></span>: 
( <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> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cohsp_1.html#T79" target="_self" title="COHSP_1:th.79">Th79</a></span>;<br/>
<a NAME="E2:140"/>
( <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> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cohsp_1.html#T79" target="_self" title="COHSP_1:th.79">Th79</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:140"/>
( <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:140"><span class="lab"><font color="Green" title="E80">A1</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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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