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<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> #);<br/>
<a NAME="E1:48_1_1"/>
 <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> #) is <a href="group_1.html#V3">Group-like</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_1_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> #) ;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D3">GROUP_1:def 3</a><br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> #);<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>
;<br/>

<b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>
;<br/>

<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K3">"</a>  as   <a href="struct_0.html#NM1">Element</a> of <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> #) ;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K3">"</a> </span>)</span>

<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="group_1.html#D6">GROUP_1:def 6</a></i>
;<br/>

<b>thus </b><font color="Maroon">c<sub>6</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font>

<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="group_1.html#D6">GROUP_1:def 6</a></i>
;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> #) as  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V3">Group-like</a>  <a href="group_1.html#L1">HGrStr</a>  ;<br/>
<a NAME="E3:48_1_1"/>
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T40">FUNCT_2:40</a></i>;<br/>
<a NAME="E4:48_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="group_2.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E5:48_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> is <a href="group_1.html#V1">strict</a>
 ;<br/>


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