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<span class="kw">let </span><font color="Maroon" title="c7">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">r</font> being   non  <a href="xxreal_0.html#V3" title="XXREAL_0:attr.3">negative</a>   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <br/>  for <font color="Olive" title="b2">p</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c7">n</font></span>)</span> holds  <font color="Olive" title="b2">p</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" title="BROUWER:func.2">Tdisk</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">r</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">r</font> be   non  <a href="xxreal_0.html#V3" title="XXREAL_0:attr.3">negative</a>   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c7">n</font></span>)</span> holds  <font color="Olive" title="b1">p</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" title="BROUWER:func.2">Tdisk</a> (<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c8">r</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c9">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c7">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">p</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" title="BROUWER:func.2">Tdisk</a> (<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c8">r</font>)</span>)</span></span><br/>





<a NAME="E1:29"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" title="BROUWER:func.2">Tdisk</a> (<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c8">r</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> (<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c8">r</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="brouwer.html#T3" title="BROUWER:th.3">BROUWER:3</a></span>;<br/>
<a NAME="E2:29"/>
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c9">p</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="toprns_1.html#T28" title="TOPRNS_1:th.28">TOPRNS_1:28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:29"/>
<font color="Maroon" title="c9">p</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" title="BROUWER:func.2">Tdisk</a> (<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c8">r</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:29"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="topreal9.html#T8" title="TOPREAL9:th.8">TOPREAL9:8</a></span>; <a class="txt" 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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