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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">V1</font>, <font color="Olive" title="b2">V2</font>, <font color="Olive" title="b3">V3</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="b4">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">V1</font>,<font color="Olive" title="b2">V2</font><br/> for <font color="Olive" title="b5">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="b3">V3</font><br/> for <font color="Olive" title="b6">b1</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b1">V1</font><br/> for <font color="Olive" title="b7">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="b8">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b3">V3</font>  st <font color="Olive" title="b4">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp; <font color="Olive" title="b5">g</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b6">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b7">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b8">b3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  holds <br/> <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">f</font></span>)</span>,<font color="Olive" title="b6">b1</font>,<font color="Olive" title="b8">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Olive" title="b4">f</font>,<font color="Olive" title="b6">b1</font>,<font color="Olive" title="b7">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Olive" title="b5">g</font>,<font color="Olive" title="b7">b2</font>,<font color="Olive" title="b8">b3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">V1</font>, <font color="Maroon" title="c3">V2</font>, <font color="Maroon" title="c4">V3</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="c2">V1</font>,<font color="Maroon" title="c3">V2</font><br/> for <font color="Olive" title="b2">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="c4">V3</font><br/> for <font color="Olive" title="b3">b1</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V1</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="Maroon" title="c3">V2</font><br/> for <font color="Olive" title="b5">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>  st <font color="Olive" title="b1">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp; <font color="Olive" title="b2">g</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">b3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  holds <br/> <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">f</font></span>)</span>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b5">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Olive" title="b2">g</font>,<font color="Olive" title="b4">b2</font>,<font color="Olive" title="b5">b3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c3">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">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="c4">V3</font><br/> for <font color="Olive" title="b2">b1</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V1</font><br/> for <font color="Olive" title="b3">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="b4">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>  st <font color="Maroon" title="c5">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp; <font color="Olive" title="b1">g</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">b3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  holds <br/> <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Olive" title="b2">b1</font>,<font color="Olive" title="b4">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Olive" title="b2">b1</font>,<font color="Olive" title="b3">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Olive" title="b1">g</font>,<font color="Olive" title="b3">b2</font>,<font color="Olive" title="b4">b3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">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="c4">V3</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">b1</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V1</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">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>  st <font color="Maroon" title="c5">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp; <font color="Maroon" title="c6">g</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">b3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  holds <br/> <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Olive" title="b1">b1</font>,<font color="Olive" title="b3">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Olive" title="b1">b1</font>,<font color="Olive" title="b2">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Olive" title="b2">b2</font>,<font color="Olive" title="b3">b3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c7">b1</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V1</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">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">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>  st <font color="Maroon" title="c5">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp; <font color="Maroon" title="c6">g</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">b3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  holds <br/> <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Olive" title="b2">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Olive" title="b1">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Olive" title="b1">b2</font>,<font color="Olive" title="b2">b3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c8">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b3</font> being   <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>  st <font color="Maroon" title="c5">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp; <font color="Maroon" title="c6">g</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">b3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  holds <br/> <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Olive" title="b1">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Olive" title="b1">b3</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c9">b3</font> be    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c4">V3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp; <font color="Maroon" title="c6">g</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">b3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  implies  <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> )</span><br/>

















<b>assume </b><a NAME="E1:62"/><i><font color="Green" title="E50">A1</font></i>: 
( <font color="Maroon" title="c5">f</font> is <a href="mod_2.html#V1" title="MOD_2:attr.1">linear</a> &amp; <font color="Maroon" title="c6">g</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"> (  not  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  or  not  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  or  not  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">b3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  or  <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E2:62"/><i><font color="Green" title="E51">A2</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">b3</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span><br/>

<b>then </b><i><font color="Green" title="E52">A3</font></i>:  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font>
<b>by </b><i><a class="ref" href="matrlin.html#T44" target="_self" title="MATRLIN:th.44">Th44</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></i>
;<br/>
<i><font color="Green" title="E53">A4</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font>
<b>by </b><i><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:62"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></i>
;<br/>
<a NAME="E5:62"/><b>then </b><i><font color="Green" title="E54">A5</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <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"><span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</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/>
<i><font color="Green" title="E55">A6</font></i>:  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">b3</font>
<b>by </b><i><a class="txt" href="#E2:62"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="matrlin.html#T44" target="_self" title="MATRLIN:th.44">Th44</a></i>
<br/>.= 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:62"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="matrlin.html#T44" target="_self" title="MATRLIN:th.44">Th44</a></i>
;<br/>
<a NAME="E7:62"/><b>then </b><i><font color="Green" title="E56">A7</font></i>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E3:62"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</a></i>;<br/>
<a NAME="E8:62"/>
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">i</font>, <font color="Maroon" title="c11">j</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"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> implies <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> )</span><br/>



<b>assume </b><a NAME="E1:62_4"/><i><font color="Green" title="E57">A8</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></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"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span><br/>

<a NAME="E2:62_4"/><b>then </b><i><font color="Green" title="E58">A9</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="matrix_1.html#D5" title="MATRIX_1:def.5">MATRIX_1:def 5</a></i>;<br/>
<a NAME="E3:62_4"/><b>then </b><i><font color="Green" title="E59">A10</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E5:62"><i><font color="Green" title="E54">A5</font></i></a>, <a class="txt" href="#E7:62"><i><font color="Green" title="E56">A7</font></i></a>, <a class="ref" href="matrix_1.html#D5" title="MATRIX_1:def.5">MATRIX_1:def 5</a></i>;<br/>
<a NAME="E4:62_4"/><i><font color="Green" title="E60">A11</font></i>: 
<font color="Maroon" title="c10">i</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#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:62_4"><i><font color="Green" title="E58">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E5:62_4"/><i><font color="Green" title="E61">A12</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</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> <font color="Maroon" title="c7">b1</font>
 
<b>by </b><i><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></i>;<br/>
<a NAME="E6:62_4"/><b>then </b><i><font color="Green" title="E62">A13</font></i>: 
<font color="Maroon" title="c10">i</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="c7">b1</font>
 
<b>by </b><i><a class="txt" href="#E4:62_4"><i><font color="Green" title="E60">A11</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c12">p1</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font><b> such that </b><br/><a NAME="E8:62_4"/><i><font color="Green" title="E63">A14</font></i>: 
( <font color="Maroon" title="c12">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font> &amp; <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">p1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">j</font> )
 <b>by </b><i><a class="txt" href="#E1:62_4"><i><font color="Green" title="E57">A8</font></i></a>, <a class="ref" href="matrix_1.html#D6" title="MATRIX_1:def.6">MATRIX_1:def 6</a></i>;<br/>
<a NAME="E9:62_4"/><i><font color="Green" title="E64">A15</font></i>: 
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:62_4"><i><font color="Green" title="E58">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E10:62_4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <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#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 
<b>by </b><i><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></i>;<br/>
<a NAME="E11:62_4"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">b1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 
<b>by </b><i><a class="txt" href="#E9:62_4"><i><font color="Green" title="E64">A15</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D4" title="MATRIX_1:def.4">MATRIX_1:def 4</a></i>;<br/>
<a NAME="E12:62_4"/><b>then </b><i><font color="Green" title="E65">A16</font></i>: 
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">b3</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E9:62_4"><i><font color="Green" title="E64">A15</font></i></a>, <a class="ref" href="matrlin.html#T44" target="_self" title="MATRLIN:th.44">Th44</a></i>;<br/>
<a NAME="E13:62_4"/><b>then </b><i><font color="Green" title="E66">A17</font></i>: 
<font color="Maroon" title="c11">j</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="c9">b3</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<i><font color="Green" title="E67">A18</font></i>: <font color="Maroon" title="c12">p1</font> = 
<span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrlin.html#K1" title="MATRLIN:func.1">/.</a> <font color="Maroon" title="c10">i</font>
<b>by </b><i><a class="txt" href="#E4:62_4"><i><font color="Green" title="E60">A11</font></i></a>, <a class="txt" href="#E8:62_4"><i><font color="Green" title="E63">A14</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c9">b3</font>
<b>by </b><i><a class="txt" href="#E6:62_4"><i><font color="Green" title="E62">A13</font></i></a>, <a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></i>
;<br/>
<a NAME="E15:62_4"/>
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E12:62_4"><i><font color="Green" title="E65">A16</font></i></a>, <a class="ref" href="matrlin.html#D9" target="_self" title="MATRLIN:def.9">Def9</a></i>;<br/>
<a NAME="E16:62_4"/><b>then </b><i><font color="Green" title="E68">A19</font></i>: 
<font color="Maroon" title="c11">j</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="c12">p1</font>
 
<b>by </b><i><a class="txt" href="#E14:62_4"><i><font color="Green" title="E67">A18</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">b2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> $1</span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>;<br/>
<b>consider </b><font color="Maroon" title="c13">d</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font><b> such that </b><br/><a NAME="E18:62_4"/><i><font color="Green" title="E69">A20</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">d</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="c8">b2</font> &amp; ( for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">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="c13">d</font> holds <br/><font color="Maroon" title="c13">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) ) )
 <b>from </b><i><a class="ref" href="finseq_2.html#S1" title="FINSEQ_2:sch.1">FINSEQ_2:sch 1</a>();<br/></i>
<a NAME="E19:62_4"/><i><font color="Green" title="E70">A21</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c13">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E18:62_4"><i><font color="Green" title="E69">A20</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E20:62_4"/><i><font color="Green" title="E71">A22</font></i>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">b2</font></span>)</span> <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="c8">b2</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E21:62_4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</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> <font color="Maroon" title="c7">b1</font>
 
<b>by </b><i><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></i>;<br/>
<a NAME="E22:62_4"/><b>then </b><i><font color="Green" title="E72">A23</font></i>: 
<font color="Maroon" title="c10">i</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#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E4:62_4"><i><font color="Green" title="E60">A11</font></i></a>, <a class="txt" href="#E5:62_4"><i><font color="Green" title="E61">A12</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<b>then </b><i><font color="Green" title="E73">A24</font></i>:  <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span>,<font color="Maroon" title="c10">i</font> = 
<span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T18" title="MATRIX_2:th.18">MATRIX_2:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrlin.html#K1" title="MATRLIN:func.1">/.</a> <font color="Maroon" title="c10">i</font>
<b>by </b><i><a class="txt" href="#E22:62_4"><i><font color="Green" title="E72">A23</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c8">b2</font>
<b>by </b><i><a class="txt" href="#E6:62_4"><i><font color="Green" title="E62">A13</font></i></a>, <a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></i>
;<br/>
<i><font color="Green" title="E74">A25</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>,<font color="Maroon" title="c11">j</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">d</font>
<b>by </b><i><a class="txt" href="#E18:62_4"><i><font color="Green" title="E69">A20</font></i></a>, <a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></i>
;<br/>
<div><i><font color="Green" title="E75">A26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="62_4_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c14">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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">k</font> &amp; <font color="Maroon" title="c14">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">d</font> implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>,<font color="Maroon" title="c11">j</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">k</font> )</span><br/><b>assume </b><a NAME="E1:62_4_4"/><i><font color="Green" title="E76">A27</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">k</font> &amp; <font color="Maroon" title="c14">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">d</font> )
 ; <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"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>,<font color="Maroon" title="c11">j</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">k</font></span><br/><a NAME="E2:62_4_4"/><b>then </b><i><font color="Green" title="E77">A28</font></i>: 
<font color="Maroon" title="c14">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="c13">d</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E3:62_4_4"/><i><font color="Green" title="E78">A30</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</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> <font color="Maroon" title="c8">b2</font>
 <b>by </b><i><a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></i>;<br/><a NAME="E4:62_4_4"/><b>then </b><i><font color="Green" title="E79">A31</font></i>: 
( <font color="Maroon" title="c14">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#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> &amp; <font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="#E6:62"><i><font color="Green" title="E55">A6</font></i></a>, <a class="txt" href="#E2:62_4"><i><font color="Green" title="E58">A9</font></i></a>, <a class="txt" href="#E18:62_4"><i><font color="Green" title="E69">A20</font></i></a>, <a class="txt" href="#E1:62_4_4"><i><font color="Green" title="E76">A27</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E5:62_4_4"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">k</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p4">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E6:62_4_4"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">k</font>,<font color="Maroon" title="c11">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 <b>by </b><i><a class="ref" href="matrix_1.html#D5" title="MATRIX_1:def.5">MATRIX_1:def 5</a></i>;<br/><b>then consider </b><font color="Maroon" title="c15">p2</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">K</font><b> such that </b><br/><a NAME="E8:62_4_4"/><i><font color="Green" title="E80">A32</font></i>: 
( <font color="Maroon" title="c15">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">k</font> &amp; <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c14">k</font>,<font color="Maroon" title="c11">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">p2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">j</font> )
 <b>by </b><i><a class="ref" href="matrix_1.html#D6" title="MATRIX_1:def.6">MATRIX_1:def 6</a></i>;<br/><a NAME="E9:62_4_4"/><i><font color="Green" title="E81">A33</font></i>: 
<font color="Maroon" title="c14">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#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E18:62_4"><i><font color="Green" title="E69">A20</font></i></a>, <a class="txt" href="#E1:62_4_4"><i><font color="Green" title="E76">A27</font></i></a>, <a class="txt" href="#E3:62_4_4"><i><font color="Green" title="E78">A30</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E10:62_4_4"/><i><font color="Green" title="E82">A34</font></i>: 
<font color="Maroon" title="c14">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="c8">b2</font>
 <b>by </b><i><a class="txt" href="#E18:62_4"><i><font color="Green" title="E69">A20</font></i></a>, <a class="txt" href="#E1:62_4_4"><i><font color="Green" title="E76">A27</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><i><font color="Green" title="E83">A35</font></i>: <font color="Maroon" title="c15">p2</font> = 
<span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrlin.html#K1" title="MATRLIN:func.1">/.</a> <font color="Maroon" title="c14">k</font>
<b>by </b><i><a class="txt" href="#E4:62_4_4"><i><font color="Green" title="E79">A31</font></i></a>, <a class="txt" href="#E8:62_4_4"><i><font color="Green" title="E80">A32</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">b2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c14">k</font></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c9">b3</font>
<b>by </b><i><a class="txt" href="#E10:62_4_4"><i><font color="Green" title="E82">A34</font></i></a>, <a class="ref" href="matrlin.html#D10" target="_self" title="MATRLIN:def.10">Def10</a></i>
;<br/><a NAME="E12:62_4_4"/><b>then </b>
<font color="Maroon" title="c11">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">p2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E12:62_4"><i><font color="Green" title="E65">A16</font></i></a>, <a class="ref" href="matrlin.html#D9" target="_self" title="MATRLIN:def.9">Def9</a></i>;<br/><a NAME="E13:62_4_4"/><b>then </b><i><font color="Green" title="E84">A36</font></i>: 
<font color="Maroon" title="c11">j</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="c15">p2</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>,<font color="Maroon" title="c11">j</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">k</font> = 
<font color="Maroon" title="c15">p2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">j</font>
<b>by </b><i><a class="txt" href="#E8:62_4_4"><i><font color="Green" title="E80">A32</font></i></a>, <a class="txt" href="#E9:62_4_4"><i><font color="Green" title="E81">A33</font></i></a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">b2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c14">k</font></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>
<b>by </b><i><a class="txt" href="#E11:62_4_4"><i><font color="Green" title="E83">A35</font></i></a>, <a class="txt" href="#E13:62_4_4"><i><font color="Green" title="E84">A36</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c13">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">k</font>
<b>by </b><i><a class="txt" href="#E18:62_4"><i><font color="Green" title="E69">A20</font></i></a>, <a class="txt" href="#E2:62_4_4"><i><font color="Green" title="E77">A28</font></i></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>
<a NAME="E26:62_4"/>
<font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V1</font>
 
;<br/>
<a NAME="E27:62_4"/><b>then </b><i><font color="Green" title="E76">A37</font></i>: 
<font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</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="c5">f</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="E28:62_4"/><i><font color="Green" title="E77">A38</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c8">b2</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> <font color="Maroon" title="c8">b2</font>
 
<b>by </b><i><a class="ref" href="matrlin.html#D9" target="_self" title="MATRLIN:def.9">Def9</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>
<b>by </b><i><a class="txt" href="#E8:62_4"><i><font color="Green" title="E63">A14</font></i></a>, <a class="txt" href="#E14:62_4"><i><font color="Green" title="E67">A18</font></i></a>, <a class="txt" href="#E16:62_4"><i><font color="Green" title="E68">A19</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>
<b>by </b><i><a class="txt" href="#E27:62_4"><i><font color="Green" title="E76">A37</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p4">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c8">b2</font></span>)</span>,<font color="Maroon" title="c8">b2</font></span>)</span></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>
<b>by </b><i><a class="ref" href="matrlin.html#T40" target="_self" title="MATRLIN:th.40">Th40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p3">(<span class="default"><a href="matrlin.html#K7" title="MATRLIN:func.7">lmlt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c8">b2</font></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c8">b2</font></span>)</span></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c9">b3</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">j</font>
<b>by </b><i><a class="txt" href="#E1:62"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="#E28:62_4"><i><font color="Green" title="E77">A38</font></i></a>, <a class="ref" href="matrlin.html#T22" target="_self" title="MATRLIN:th.22">Th22</a></i>
<br/>.= 
 <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">b1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin.html#K11" title="MATRLIN:func.11">|--</a> <font color="Maroon" title="c8">b2</font></span>)</span>,<font color="Maroon" title="c13">d</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:62"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="#E13:62_4"><i><font color="Green" title="E66">A17</font></i></a>, <a class="txt" href="#E18:62_4"><i><font color="Green" title="E69">A20</font></i></a>, <a class="txt" href="#E20:62_4"><i><font color="Green" title="E71">A22</font></i></a>, <a class="txt" href="#E28:62_4"><i><font color="Green" title="E77">A38</font></i></a>, <a class="ref" href="matrlin.html#T42" target="_self" title="MATRLIN:th.42">Th42</a>, <a class="txt" href="#E19:62_4"><i><font color="Green" title="E70">A21</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span>,<font color="Maroon" title="c10">i</font></span>)</span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>,<font color="Maroon" title="c11">j</font></span>)</span>
<b>by </b><i><a class="txt" href="#E23:62_4"><i><font color="Green" title="E73">A24</font></i></a>, <a class="txt" href="#E24:62_4"><i><font color="Green" title="E74">A25</font></i></a>, <a class="txt" href="#E25:62_4"><i><font color="Green" title="E75">A26</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c10">i</font>,<font color="Maroon" title="c11">j</font>
<b>by </b><i><a class="txt" href="#E3:62"><i><font color="Green" title="E52">A3</font></i></a>, <a class="txt" href="#E3:62_4"><i><font color="Green" title="E59">A10</font></i></a>, <a class="ref" href="matrix_3.html#D4" title="MATRIX_3:def.4">MATRIX_3:def 4</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="E9:62"/>
 <a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin.html#K12" title="MATRLIN:func.12">AutMt</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E4:62"><i><font color="Green" title="E53">A4</font></i></a>, <a class="txt" href="#E7:62"><i><font color="Green" title="E56">A7</font></i></a>, <a class="ref" href="matrix_1.html#T21" title="MATRIX_1:th.21">MATRIX_1:21</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>
