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<span class="kw">let </span><font color="Maroon" title="c1">V1</font>, <font color="Maroon" title="c2">V2</font> be   <a href="vectsp_7.html#V3" title="VECTSP_7:attr.3">free</a>   <a href="zmodul03.html#V1" title="ZMODUL03:attr.1">finite-rank</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">V1</font>,<font color="Maroon" title="c2">V2</font><br/>  for <font color="Olive" title="b2">b1</font> being    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c1">V1</font><br/>  for <font color="Olive" title="b3">b2</font> being    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V2</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> <a href="zmatrlin.html#K10" title="ZMATRLIN:func.10">AutMt</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">b1</font>,<font color="Olive" title="b3">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">V1</font>,<font color="Maroon" title="c2">V2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b1</font> being    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c1">V1</font><br/>  for <font color="Olive" title="b2">b2</font> being    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V2</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> <a href="zmatrlin.html#K10" title="ZMATRLIN:func.10">AutMt</a> (<font color="Maroon" title="c3">f</font>,<font color="Olive" title="b1">b1</font>,<font color="Olive" title="b2">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">b1</font> be    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c1">V1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b2</font> being    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V2</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> <a href="zmatrlin.html#K10" title="ZMATRLIN:func.10">AutMt</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Olive" title="b1">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">b2</font> be    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c2">V2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies  <a href="zmatrlin.html#K10" title="ZMATRLIN:func.10">AutMt</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>









<span class="kw">assume </span><a NAME="E1:50"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="zmatrlin.html#K10" title="ZMATRLIN:func.10">AutMt</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E2:50"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="zmatrlin.html#K10" title="ZMATRLIN:func.10">AutMt</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmatrlin.html#D8" target="_self" onmouseover="rs('zmatrlin/D8')" onmouseout="rh()">Def8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:50"/>
 <a href="zmatrlin.html#K10" title="ZMATRLIN:func.10">AutMt</a> (<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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