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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V2</font>, <font color="Olive" title="b2">V1</font> being <a href="matrlin.html#V2" title="MATRLIN:attr.2">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">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">V1</font>,<font color="Olive" title="b1">V2</font><br/> for <font color="Olive" title="b4">a</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b5">p</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Olive" title="b2">V1</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">p</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">a</font> &amp; <font color="Olive" title="b3">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> holds <br/><font color="Olive" title="b3">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Olive" title="b4">a</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Olive" title="b5">p</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">V2</font>, <font color="Maroon" title="c3">V1</font> be  <a href="matrlin.html#V2" title="MATRLIN:attr.2">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c2">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><br/> for <font color="Olive" title="b3">p</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c3">V1</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">p</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">a</font> &amp; <font color="Olive" title="b1">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> holds <br/><font color="Olive" title="b1">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Olive" title="b2">a</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Olive" title="b3">p</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c2">V2</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">a</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b2">p</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c3">V1</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">p</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">a</font> &amp; <font color="Maroon" title="c4">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> holds <br/><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Olive" title="b1">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Olive" title="b2">p</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c3">V1</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">p</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">a</font> &amp; <font color="Maroon" title="c4">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> holds <br/><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Olive" title="b1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Olive" title="b1">p</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">p</font> be   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c3">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">p</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">a</font> &amp; <font color="Maroon" title="c4">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> implies <font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span> )</span><br/>











<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E25">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">p</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">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> or <font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E2:31"/><i><font color="Green" title="E26">A2</font></i>: 
<font color="Maroon" title="c4">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span></span><br/>

<a NAME="E3:31"/><i><font color="Green" title="E27">A3</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">a</font>
 
<b>by </b><i><a class="txt" href="matrlin.html#E1:31"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E4:31"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">V1</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:31"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E6:31"/><b>then </b><i><font color="Green" title="E28">A4</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T46" title="RELAT_1:th.46">RELAT_1:46</a></i>;<br/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span> = 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font>
<b>by </b><i><a class="txt" href="matrlin.html#E3:31"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="matrlin.html#T16" target="_self" title="MATRLIN:th.16">Th16</a></i>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrlin.html#E3:31"><i><font color="Green" title="E27">A3</font></i></a>, <a class="txt" href="matrlin.html#E6:31"><i><font color="Green" title="E28">A4</font></i></a>, <a class="ref" href="matrlin.html#T16" target="_self" title="MATRLIN:th.16">Th16</a></i>
;<br/>
<a NAME="E8:31"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E9:31"/><b>then </b><i><font color="Green" title="E29">A5</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T37" title="FINSEQ_2:th.37">FINSEQ_2:37</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font> )</span><br/><b>assume </b><a NAME="E1:31_2"/>
<font color="Maroon" title="c7">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font></span><br/><a NAME="E2:31_2"/><b>then </b><i><font color="Green" title="E30">A6</font></i>: 
<font color="Maroon" title="c7">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 ;<br/><a NAME="E3:31_2"/><i><font color="Green" title="E31">A7</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T44" title="RELAT_1:th.44">RELAT_1:44</a></i>;<br/><a NAME="E4:31_2"/><b>then </b>
<font color="Maroon" title="c7">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="matrlin.html#E2:31_2"><i><font color="Green" title="E30">A6</font></i></a></i>;<br/><a NAME="E5:31_2"/><b>then </b><i><font color="Green" title="E32">A8</font></i>: 
<font color="Maroon" title="c7">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">p</font>
 <b>by </b><i><a class="txt" href="matrlin.html#E3:31"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="matrlin.html#T16" target="_self" title="MATRLIN:th.16">Th16</a></i>;<br/><a NAME="E6:31_2"/><b>then </b><i><font color="Green" title="E33">A9</font></i>: 
<font color="Maroon" title="c5">a</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font>
 <b>by </b><i><a class="txt" href="matrlin.html#E3:31"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/><a NAME="E7:31_2"/><i><font color="Green" title="E34">A10</font></i>: 
<font color="Maroon" title="c6">p</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font>
 <b>by </b><i><a class="txt" href="matrlin.html#E5:31_2"><i><font color="Green" title="E32">A8</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/><b>set </b><font color="Maroon" title="c8">P</font> = <font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font>;<br/><a NAME="E8:31_2"/><i><font color="Green" title="E35">A11</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font>
 <b>by </b><i><a class="txt" href="matrlin.html#E6:31"><i><font color="Green" title="E28">A4</font></i></a>, <a class="txt" href="matrlin.html#E5:31_2"><i><font color="Green" title="E32">A8</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/><a NAME="E9:31_2"/><i><font color="Green" title="E36">A12</font></i>: 
<font color="Maroon" title="c7">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="matrlin.html#E3:31"><i><font color="Green" title="E27">A3</font></i></a>, <a class="txt" href="matrlin.html#E6:31"><i><font color="Green" title="E28">A4</font></i></a>, <a class="txt" href="matrlin.html#E5:31_2"><i><font color="Green" title="E32">A8</font></i></a>, <a class="ref" href="matrlin.html#T16" target="_self" title="MATRLIN:th.16">Th16</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font> = 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font></span>)</span>
<b>by </b><i><a class="txt" href="matrlin.html#E2:31_2"><i><font color="Green" title="E30">A6</font></i></a>, <a class="ref" href="funct_1.html#T22" title="FUNCT_1:th.22">FUNCT_1:22</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <font color="Maroon" title="c3">V1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrlin.html#E2:31_2"><i><font color="Green" title="E30">A6</font></i></a>, <a class="txt" href="matrlin.html#E3:31_2"><i><font color="Green" title="E31">A7</font></i></a>, <a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrlin.html#E6:31_2"><i><font color="Green" title="E33">A9</font></i></a>, <a class="txt" href="matrlin.html#E7:31_2"><i><font color="Green" title="E34">A10</font></i></a>, <a class="ref" href="vectsp_1.html#D24" title="VECTSP_1:def.24">VECTSP_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">p</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="matrlin.html#E2:31"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="mod_2.html#D5" title="MOD_2:def.5">MOD_2:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font></span>)</span>
<b>by </b><i><a class="txt" href="matrlin.html#E5:31_2"><i><font color="Green" title="E32">A8</font></i></a>, <a class="txt" href="matrlin.html#E7:31_2"><i><font color="Green" title="E34">A10</font></i></a>, <a class="txt" href="matrlin.html#E8:31_2"><i><font color="Green" title="E35">A11</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <font color="Maroon" title="c2">V2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font></span>)</span>
<b>by </b><i><a class="txt" href="matrlin.html#E6:31_2"><i><font color="Green" title="E33">A9</font></i></a>, <a class="txt" href="matrlin.html#E8:31_2"><i><font color="Green" title="E35">A11</font></i></a>, <a class="ref" href="vectsp_1.html#D24" title="VECTSP_1:def.24">VECTSP_1:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">k</font>
<b>by </b><i><a class="txt" href="matrlin.html#E9:31_2"><i><font color="Green" title="E36">A12</font></i></a>, <a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:31"/>
<font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <font color="Maroon" title="c5">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c6">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="matrlin.html#E9:31"><i><font color="Green" title="E29">A5</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
