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<b>let </b><font color="Maroon">x</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">y</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:24_1_2"/><i><font color="Green">E32</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font>
 <b>and </b><br/><a NAME="E2:24_1_2"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">n</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">x</font> holds <br/>for <font color="Olive">h</font> being non <a href="xboole_0.html#V1">empty</a> <a href="unialg_1.html#V1" target="_self">homogeneous</a> <a href="partfun1.html#NM1">PartFunc</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="finseq_1.html#K13">*</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>  st <font color="Olive">h</font> <a href="hidden.html#R1">=</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> holds <br/><font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K3" target="_self">arity</a> <font color="Olive">h</font>
 <b>and </b><br/><a NAME="E3:24_1_2"/><i><font color="Green">E51</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font>
 <b>and </b><br/><a NAME="E4:24_1_2"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">n</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">y</font> holds <br/>for <font color="Olive">h</font> being non <a href="xboole_0.html#V1">empty</a> <a href="unialg_1.html#V1" target="_self">homogeneous</a> <a href="partfun1.html#NM1">PartFunc</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="finseq_1.html#K13">*</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>  st <font color="Olive">h</font> <a href="hidden.html#R1">=</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> holds <br/><font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K3" target="_self">arity</a> <font color="Olive">h</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:24_1_2_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> &amp; <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> )
 ;<br/><a NAME="E2:24_1_2_1"/><b>then </b>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E3:24_1_2_1"/><b>then </b><i><font color="Green">E53</font></i>: 
( <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">x</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">y</font> )
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon">h</font> = the <a href="unialg_1.html#U1" target="_self">charact</a> of <font color="Maroon">U1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="unialg_1.html#V1" target="_self">homogeneous</a> <a href="partfun1.html#NM1">PartFunc</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="finseq_1.html#K13">*</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <b>by </b><i>, , <a class="ref" href="funct_1.html#D15">FUNCT_1:def 15</a></i>;<br/><a NAME="E5:24_1_2_1"/>
( <font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K3" target="_self">arity</a> <font color="Maroon">h</font> &amp; <font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K3" target="_self">arity</a> <font color="Maroon">h</font> )
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E6:24_1_2_1"/>
<font color="Maroon">x</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:24_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


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