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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">V</font> being  <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b2">a</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b3">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font><br/> for <font color="Olive" title="b4">L</font> being   <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b4">L</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b3">A</font> holds <br/><font color="Olive" title="b4">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Olive" title="b2">a</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b3">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b2">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font><br/> for <font color="Olive" title="b3">L</font> being   <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b3">L</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b2">A</font> holds <br/><font color="Olive" title="b3">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Olive" title="b1">a</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b2">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font><br/> for <font color="Olive" title="b2">L</font> being   <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b2">L</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b2">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">a</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Olive" title="b1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">A</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">L</font> being   <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">L</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c4">A</font> holds <br/><font color="Olive" title="b1">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">a</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c4">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">L</font> be    <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">L</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c4">A</font> implies <font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">a</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c4">A</font> )</span><br/>









<span class="kw">assume </span><a NAME="E1:70"/>
<font color="Maroon" title="c5">L</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c4">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">a</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c4">A</font></span><br/>

<a NAME="E2:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A1</font></span>: 
 <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c5">L</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#D7" target="_self" title="RMOD_4:def.7">Def7</a></span>;<br/>
<a NAME="E3:70"/>
 <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c5">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#T58" target="_self" title="RMOD_4:th.58">Th58</a></span>;<br/>
<a NAME="E4:70"/><span class="kw">then </span>
 <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:70"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:70"/>
<font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">a</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c4">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#D7" target="_self" title="RMOD_4:def.7">Def7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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