<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">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#M2" title="HIDDEN:mode.2">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/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#M2" title="HIDDEN:mode.2">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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#M2" title="HIDDEN:mode.2">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/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:35"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<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> 
 <span class="kw">and </span><br/><a NAME="E2:35"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">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/>

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E3:35"/>
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">then </span><span class="kw">reconsider </span><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="E5:35"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="lmod_7.html#D11" target="_self" onmouseover="rs('lmod_7/D11')" onmouseout="rh()">Def11</a></span>;<br/>
<a NAME="E6:35"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:35"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lmod_7.html#D11" target="_self" onmouseover="rs('lmod_7/D11')" onmouseout="rh()">Def11</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
