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<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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"> for <font color="Olive" title="b1">f1</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font><br/> for <font color="Olive" title="b2">f2</font> being non <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>  <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Olive" title="b2">f2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Olive" title="b2">f2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">f2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">f1</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f2</font> being non <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>  <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Olive" title="b1">f2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Olive" title="b1">f2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">f2</font> be  non <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>  <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c3">f2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f2</font></span>)</span></span><br/>





<a NAME="E1:79"/>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f2</font>
 
<b>by </b><i><a class="ref" href="realset1.html#T13" title="REALSET1:th.13">REALSET1:13</a></i>;<br/>
<a NAME="E2:79"/><b>then </b><i><font color="Green" title="E57">A1</font></i>: 
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f2</font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E3:79"/><b>then </b><i><font color="Green" title="E58">A2</font></i>: 
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<a NAME="E4:79"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c3">f2</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="graph_2.html#T13" target="_self" title="GRAPH_2:th.13">Th13</a></i>;<br/>
<a NAME="E5:79"/><b>then </b>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c3">f2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="graph_2.html#E3:79"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c3">f2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c3">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="graph_2.html#K4" title="GRAPH_2:func.4">^'</a> <font color="Maroon" title="c3">f2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_4.html#T24" title="FINSEQ_4:th.24">FINSEQ_4:24</a></i>
<br/>.= 
<font color="Maroon" title="c3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f2</font></span>)</span>
<b>by </b><i><a class="txt" href="graph_2.html#E2:79"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="graph_2.html#T16" target="_self" title="GRAPH_2:th.16">Th16</a></i>
<br/>.= 
<font color="Maroon" title="c3">f2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">f2</font></span>)</span>
<b>by </b><i><a class="txt" href="graph_2.html#E2:79"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="finseq_4.html#T24" title="FINSEQ_4:th.24">FINSEQ_4:24</a></i>
;<br/> <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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