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<b>consider </b><font color="Maroon">c<sub>1</sub></font> being  <a href="vectsp_1.html#V3">strict</a> <a href="vectsp_1.html#NM2">Field</a>;<br/>
<a NAME="E2:49_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>3</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Olive">b<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>4</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>4</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Olive">b<sub>3</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gcd_1.html#E39"><i><font color="Green">Lemma35</font></i></a></i>;<br/>
<a NAME="E3:49_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> is <a href="gcd_1.html#V3" target="_self">gcd-like</a>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D11" target="_self">Def11</a></i>;<br/>
<b>hence </b><a NAME="E4:49_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3">empty</a>  <a href="vectsp_1.html#L1">multLoopStr</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="gcd_1.html#V3" target="_self">gcd-like</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="group_1.html#V4">associative</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="group_1.html#V7">commutative</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="group_1.html#V2">unital</a> )
 ;<br/>


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