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<b>let </b><font color="Maroon" title="c1">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> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="vectmetr.html#K5" title="VECTMETR:func.5">IsomGroup</a> <font color="Maroon" title="c1">n</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c3">g</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="vectmetr.html#K4" title="VECTMETR:func.4">RLMSpace</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="vectmetr.html#K4" title="VECTMETR:func.4">RLMSpace</a> <font color="Maroon" title="c1">n</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:34"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font>
 ;<br/>

<a NAME="E2:34"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="vectmetr.html#K5" title="VECTMETR:func.5">IsomGroup</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
;<br/>
<a NAME="E3:34"/><b>then </b><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="vectmetr.html#K2" title="VECTMETR:func.2">ISOM</a> <span class="p1">(<span class="default"><a href="vectmetr.html#K4" title="VECTMETR:func.4">RLMSpace</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="vectmetr.html#D9" target="_self" title="VECTMETR:def.9">Def9</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">f1</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="vectmetr.html#K4" title="VECTMETR:func.4">RLMSpace</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="vectmetr.html#K4" title="VECTMETR:func.4">RLMSpace</a> <font color="Maroon" title="c1">n</font></span>)</span><b> such that </b><br/><a NAME="E5:34"/><i><font color="Green" title="E17">A3</font></i>: 
<font color="Maroon" title="c4">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font>
 <b>and </b><br/><a NAME="E6:34"/><i><font color="Green" title="E18">A4</font></i>: 
<font color="Maroon" title="c4">f1</font> is <a href="vectmetr.html#V3" title="VECTMETR:attr.3">isometric</a>
 <b>by </b><i><a class="ref" href="vectmetr.html#D4" target="_self" title="VECTMETR:def.4">Def4</a></i>;<br/>
<a NAME="E7:34"/>
<font color="Maroon" title="c3">g</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  is <a href="vectmetr.html#V3" title="VECTMETR:attr.3">isometric</a>
 
<b>by </b><i><a class="txt" href="vectmetr.html#E1:34"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="vectmetr.html#E5:34"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="vectmetr.html#E6:34"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="vectmetr.html#T3" target="_self" title="VECTMETR:th.3">Th3</a></i>;<br/>
<a NAME="E8:34"/><b>then </b><i><font color="Green" title="E19">A5</font></i>: 
<font color="Maroon" title="c3">g</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="vectmetr.html#K2" title="VECTMETR:func.2">ISOM</a> <span class="p1">(<span class="default"><a href="vectmetr.html#K4" title="VECTMETR:func.4">RLMSpace</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="vectmetr.html#D4" target="_self" title="VECTMETR:def.4">Def4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">g1</font> = <font color="Maroon" title="c3">g</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="vectmetr.html#K5" title="VECTMETR:func.5">IsomGroup</a> <font color="Maroon" title="c1">n</font></span>)</span> <b>by </b><i><a class="ref" href="vectmetr.html#D9" target="_self" title="VECTMETR:def.9">Def9</a></i>;<br/>
<a NAME="E10:34"/><i><font color="Green" title="E20">A6</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="vectmetr.html#K4" title="VECTMETR:func.4">RLMSpace</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<b>by </b><i><a class="txt" href="vectmetr.html#E6:34"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="vectmetr.html#D3" target="_self" title="VECTMETR:def.3">Def3</a></i>;<br/>
<a NAME="E11:34"/><i><font color="Green" title="E21">A7</font></i>: 
<font color="Maroon" title="c4">f1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="vectmetr.html#E6:34"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="vectmetr.html#T2" target="_self" title="VECTMETR:th.2">Th2</a></i>;<br/>
<i><font color="Green" title="E22">A8</font></i>: <font color="Maroon" title="c2">f</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">g1</font> = 
<font color="Maroon" title="c4">f1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="vectmetr.html#E3:34"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="vectmetr.html#E5:34"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="vectmetr.html#E8:34"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="vectmetr.html#D9" target="_self" title="VECTMETR:def.9">Def9</a></i>
<br/>.= 
 <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <span class="p1">(<span class="default"><a href="vectmetr.html#K4" title="VECTMETR:func.4">RLMSpace</a> <font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="txt" href="vectmetr.html#E1:34"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="vectmetr.html#E5:34"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="vectmetr.html#E10:34"><i><font color="Green" title="E20">A6</font></i></a>, <a class="txt" href="vectmetr.html#E11:34"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="tops_2.html#T65" title="TOPS_2:th.65">TOPS_2:65</a></i>
<br/>.= 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="vectmetr.html#K5" title="VECTMETR:func.5">IsomGroup</a> <font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="ref" href="vectmetr.html#T10" target="_self" title="VECTMETR:th.10">Th10</a></i>
;<br/>
<font color="Maroon" title="c5">g1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c2">f</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f1</font>
<b>by </b><i><a class="txt" href="vectmetr.html#E3:34"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="vectmetr.html#E5:34"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="vectmetr.html#E8:34"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="vectmetr.html#D9" target="_self" title="VECTMETR:def.9">Def9</a></i>
<br/>.= 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f1</font></span>)</span>
<b>by </b><i><a class="txt" href="vectmetr.html#E1:34"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="vectmetr.html#E5:34"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="vectmetr.html#E10:34"><i><font color="Green" title="E20">A6</font></i></a>, <a class="txt" href="vectmetr.html#E11:34"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="tops_2.html#T65" title="TOPS_2:th.65">TOPS_2:65</a></i>
<br/>.= 
 <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <span class="p1">(<span class="default"><a href="vectmetr.html#K4" title="VECTMETR:func.4">RLMSpace</a> <font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
<br/>.= 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="vectmetr.html#K5" title="VECTMETR:func.5">IsomGroup</a> <font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="ref" href="vectmetr.html#T10" target="_self" title="VECTMETR:th.10">Th10</a></i>
;<br/>
<b>hence </b><a NAME="E14:34"/>
<font color="Maroon" title="c2">f</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> 
 <b>by </b><i><a class="txt" href="vectmetr.html#E12:34"><i><font color="Green" title="E22">A8</font></i></a>, <a class="ref" href="group_1.html#T12" title="GROUP_1:th.12">GROUP_1:12</a></i>;<br/>


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