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<b>let </b><font color="Maroon" title="c1">K</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V</font> being  <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b2">A1</font>, <font color="Olive" title="b3">A2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b2">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b2">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">A2</font> holds <br/>for <font color="Olive" title="b4">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b4">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Olive" title="b2">A1</font> holds <br/><font color="Olive" title="b4">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Olive" title="b3">A2</font></span><br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A1</font>, <font color="Olive" title="b2">A2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">A2</font> holds <br/>for <font color="Olive" title="b3">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Olive" title="b1">A1</font> holds <br/><font color="Olive" title="b3">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Olive" title="b2">A2</font></span><br/><b>let </b><font color="Maroon" title="c3">A1</font>, <font color="Maroon" title="c4">A2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A2</font> implies for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Maroon" title="c3">A1</font> holds <br/><font color="Olive" title="b1">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Maroon" title="c4">A2</font> )</span><br/>







<b>assume </b><a NAME="E1:35"/><i><font color="Green" title="E11">A1</font></i>: 
( <font color="Maroon" title="c3">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Maroon" title="c3">A1</font> holds <br/><font color="Olive" title="b1">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Maroon" title="c4">A2</font></span><br/>

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Maroon" title="c3">A1</font> implies <font color="Maroon" title="c5">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Maroon" title="c4">A2</font> )</span><br/>

<b>assume </b><a NAME="E2:35"/>
<font color="Maroon" title="c5">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Maroon" title="c3">A1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Maroon" title="c4">A2</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c6">a</font> = <font color="Maroon" title="c5">x</font> as    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Maroon" title="c3">A1</font> ;<br/>
<a NAME="E4:35"/>
<font color="Maroon" title="c6">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A1</font>
 
<b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="lmod_7.html#D11" target="_self" title="LMOD_7:def.11">Def11</a></i>;<br/>
<a NAME="E5:35"/><b>then </b>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A2</font>
 
<b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:35"/>
<font color="Maroon" title="c5">x</font> is    <a href="lmod_7.html#M9" title="LMOD_7:mode.9">Vector</a> of <font color="Maroon" title="c4">A2</font>
 <b>by </b><i><a class="ref" href="lmod_7.html#D11" target="_self" title="LMOD_7:def.11">Def11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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