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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="gtarski1.html#V9" title="GTARSKI1:attr.9">satisfying_Tarski-model</a>   <a href="gtarski1.html#L1" title="GTARSKI1:struct.1">TarskiGeometryStruct</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">a9</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>  st  <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp;  <a href="gtarski1.html#R6" title="GTARSKI1:pred.6">Collinear</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> holds <br/> <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">a9</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font> be   <a href="gtarski1.html#NM1" title="GTARSKI1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> &amp;  <a href="gtarski1.html#R6" title="GTARSKI1:pred.6">Collinear</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">a9</font> implies  <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:19"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
 <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">and </span><br/><a NAME="E2:19"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">and </span><br/><a NAME="E3:19"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
 <a href="gtarski1.html#R6" title="GTARSKI1:pred.6">Collinear</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">a9</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c4">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>)</span></a><div class="add"><a NAME="E1:19_1"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a>  <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c4">b</font>), <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski3.html#T105" onmouseover="rs('gtarski3/T105')" onmouseout="rh()">GTARSKI3:105</a></span>;<br/><span class="kw">hence </span><a NAME="E2:19_1"/>
<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font> <a href="gtarski1.html#R2" title="GTARSKI1:pred.2">equiv</a> <font color="Maroon" title="c4">b</font>, <a href="gtarski3.html#K3" title="GTARSKI3:func.3">reflection</a> (<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gtarski4.html#T14" target="_self" onmouseover="rs('gtarski4/T14')" onmouseout="rh()">Lem01</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:19"/>
 <a href="gtarski4.html#R1" title="GTARSKI4:pred.1">right_angle</a> <font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E2:19"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="txt" href="#E3:19"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="gtarski3.html#T53" onmouseover="rs('gtarski3/T53')" onmouseout="rh()">GTARSKI3:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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