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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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">f</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   st ( <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> or <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 3 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c2">n</font> ) &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">f</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ; <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="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> or <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 3 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c2">n</font> ) &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">i</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:66"/><span class="lab"><font color="Green" title="E54">A1</font></span>: 
( ( <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> or <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 3 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c2">n</font> ) &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">i</font></span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">i</font> = 
<span class="p1">(<span class="default"><a href="graphsp.html#K18" title="GRAPHSP:func.18">Relax</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="graphsp.html#D15" target="_self" title="GRAPHSP:def.15">Def15</a></span>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="ref" href="graphsp.html#D14" target="_self" title="GRAPHSP:def.14">Def14</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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