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<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V3</font>, <font color="Olive" title="b2">V2</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b3">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">V2</font>,<font color="Olive" title="b1">V3</font><br/>  for <font color="Olive" title="b4">b2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b2">V2</font><br/>  for <font color="Olive" title="b5">a</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">b2</font> &amp; <font color="Olive" title="b3">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Olive" title="b3">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  holds <br/><font color="Olive" title="b3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Olive" title="b5">a</font>,<font color="Olive" title="b4">b2</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Olive" title="b5">a</font>,<span class="p2">(<span class="default"><font color="Olive" title="b3">g</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Olive" title="b4">b2</font></span>)</span>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V3</font>, <font color="Maroon" title="c3">V2</font> be   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V2</font>,<font color="Maroon" title="c2">V3</font><br/>  for <font color="Olive" title="b2">b2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c3">V2</font><br/>  for <font color="Olive" title="b3">a</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">b2</font> &amp; <font color="Olive" title="b1">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Olive" title="b1">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  holds <br/><font color="Olive" title="b1">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">b2</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Olive" title="b3">a</font>,<span class="p2">(<span class="default"><font color="Olive" title="b1">g</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Olive" title="b2">b2</font></span>)</span>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">g</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V2</font>,<font color="Maroon" title="c2">V3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b2</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c3">V2</font><br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">b2</font> &amp; <font color="Maroon" title="c4">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Maroon" title="c4">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  holds <br/><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">b2</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Olive" title="b2">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Olive" title="b1">b2</font></span>)</span>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">b2</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c3">V2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c4">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Maroon" title="c4">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  holds <br/><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Olive" title="b1">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c5">b2</font></span>)</span>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">a</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c4">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Maroon" title="c4">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  implies <font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Maroon" title="c6">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c5">b2</font></span>)</span>)</span>)</span> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:27"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">b2</font>
 <span class="kw">and </span><br/><a NAME="E2:27"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
( <font color="Maroon" title="c4">g</font> is  <a href="grcat_1.html#V1" title="GRCAT_1:attr.1">additive</a>  &amp; <font color="Maroon" title="c4">g</font> is  <a href="mod_2.html#V1" title="MOD_2:attr.1">homogeneous</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Maroon" title="c6">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c5">b2</font></span>)</span>)</span>)</span></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span></span>)</span> = 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="matrlin.html#T16" target="_self" title="MATRLIN:th.16">Th20</a></span>
<br/>.= 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="matrlin.html#K5" title="MATRLIN:func.5">lmlt</a> (<font color="Maroon" title="c6">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c5">b2</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="matrlin.html#T17" target="_self" title="MATRLIN:th.17">Th21</a></span>
; <a class="txt" 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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