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<b>consider </b><font color="Maroon" title="c1">F</font> being  <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a> <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/>
<a NAME="E2:50_1_1"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font>  ex <font color="Olive" title="b3">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font> st <br/>( <font color="Olive" title="b3">z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b3">z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Olive" title="b2">y</font> &amp; ( for <font color="Olive" title="b4">zz</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font>  st <font color="Olive" title="b4">zz</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b4">zz</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Olive" title="b2">y</font> holds <br/><font color="Olive" title="b4">zz</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Olive" title="b3">z</font> ) )
 
<b>by </b><i><a class="txt" href="gcd_1.html#E39"><i><font color="Green" title="E35">Lm1</font></i></a></i>;<br/>
<a NAME="E3:50_1_1"/><b>then </b>
<font color="Maroon" title="c1">F</font> is <a href="gcd_1.html#V3" title="GCD_1:attr.3">gcd-like</a>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D11" target="_self" title="GCD_1:def.11">Def11</a></i>;<br/>
<b>hence </b><a NAME="E4:50_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="algstr_0.html#L5" title="ALGSTR_0:struct.5">multLoopStr_0</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="gcd_1.html#V3" title="GCD_1:attr.3">gcd-like</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a> )
 ;<br/>


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