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<span class="kw">let </span><font color="Maroon" title="c1">R</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">R</font><br/>  for <font color="Olive" title="b2">W1</font>, <font color="Olive" title="b3">W2</font>, <font color="Olive" title="b4">W3</font> being   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b2">W1</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b3">W2</font> holds <br/><font color="Olive" title="b2">W1</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b3">W2</font> <a href="zmodul01.html#K1" title="ZMODUL01:func.1">+</a> <font color="Olive" title="b4">W3</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">R</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">W1</font>, <font color="Olive" title="b2">W2</font>, <font color="Olive" title="b3">W3</font> being   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">W1</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b2">W2</font> holds <br/><font color="Olive" title="b1">W1</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b2">W2</font> <a href="zmodul01.html#K1" title="ZMODUL01:func.1">+</a> <font color="Olive" title="b3">W3</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">W1</font>, <font color="Maroon" title="c4">W2</font>, <font color="Maroon" title="c5">W3</font> be   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</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">W1</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Maroon" title="c4">W2</font> implies <font color="Maroon" title="c3">W1</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Maroon" title="c4">W2</font> <a href="zmodul01.html#K1" title="ZMODUL01:func.1">+</a> <font color="Maroon" title="c5">W3</font> )</span><br/>









<a NAME="E1:53"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<font color="Maroon" title="c4">W2</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Maroon" title="c4">W2</font> <a href="zmodul01.html#K1" title="ZMODUL01:func.1">+</a> <font color="Maroon" title="c5">W3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul01.html#T97" onmouseover="rs('zmodul01/T97')" onmouseout="rh()">ZMODUL01:97</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:53"/>
<font color="Maroon" title="c3">W1</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Maroon" title="c4">W2</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">W1</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Maroon" title="c4">W2</font> <a href="zmodul01.html#K1" title="ZMODUL01:func.1">+</a> <font color="Maroon" title="c5">W3</font></span><br/>

<span class="kw">hence </span><a NAME="E3:53"/>
<font color="Maroon" title="c3">W1</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Maroon" title="c4">W2</font> <a href="zmodul01.html#K1" title="ZMODUL01:func.1">+</a> <font color="Maroon" title="c5">W3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="zmodul01.html#T42" onmouseover="rs('zmodul01/T42')" onmouseout="rh()">ZMODUL01:42</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/>


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