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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="prvect_2.html#NM3" title="PRVECT_2:NM.3">RealNormSpace-Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="prvect_2.html#K14" title="PRVECT_2:func.14">product</a> <font color="Maroon" title="c1">G</font></span>)</span><br/>  for <font color="Olive" title="b3">r0</font>, <font color="Olive" title="b4">p0</font>, <font color="Olive" title="b5">q0</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="prvect_2.html#K4" title="PRVECT_2:func.4">carr</a> <font color="Maroon" title="c1">G</font></span>)</span>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">p0</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">q0</font> holds <br/>( <font color="Olive" title="b1">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">r0</font> iff  for <font color="Olive" title="b6">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">G</font> holds  <font color="Olive" title="b3">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b6">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b6">i</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="prvect_2.html#K14" title="PRVECT_2:func.14">product</a> <font color="Maroon" title="c1">G</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">r0</font>, <font color="Olive" title="b2">p0</font>, <font color="Olive" title="b3">q0</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="prvect_2.html#K4" title="PRVECT_2:func.4">carr</a> <font color="Maroon" title="c1">G</font></span>)</span>  st <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">p0</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q0</font> holds <br/>( <font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r0</font> iff  for <font color="Olive" title="b4">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">G</font> holds  <font color="Olive" title="b1">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b4">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b4">i</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">r0</font>, <font color="Maroon" title="c5">p0</font>, <font color="Maroon" title="c6">q0</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="prvect_2.html#K4" title="PRVECT_2:func.4">carr</a> <font color="Maroon" title="c1">G</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p0</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q0</font> implies ( <font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r0</font> iff  for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">G</font> holds  <font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:22"/><span class="lab"><font color="Green" title="E18">AS0</font></span>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p0</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q0</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r0</font> iff  for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">G</font> holds  <font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">qq0</font> = <span class="p1">(<span class="default"><a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">q</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="prvect_2.html#K4" title="PRVECT_2:func.4">carr</a> <font color="Maroon" title="c1">G</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="ndiff_5.html#T10" target="_self" title="NDIFF_5:th.10">LM001</a></span>;<br/>
<a NAME="E3:22"/><span class="lab"><font color="Green" title="E19">X0</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">q</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></span>;<br/>
<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">G</font> holds  <font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> ) implies <font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r0</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:22_1"/><span class="lab"><font color="Green" title="E20">AS1</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r0</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">G</font> holds  <font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span></span><br/><span class="kw">thus </span><a NAME="E2:22_1"/>
 for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">G</font> holds  <font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span></span><br/>

<a NAME="E1:22_1_1"/><span class="lab"><font color="Green" title="E21">X1</font></span>: 
<font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">qq0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ndiff_5.html#T12" target="_self" title="NDIFF_5:th.12">ADD1</a>, <a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E20">AS1</font></span></a>, <a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E18">AS0</font></span></a>, <a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E19">X0</font></span></a></span>;<br/>
<a NAME="E2:22_1_1"/>
 <a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1 is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></span>;<br/>
<a NAME="E3:22_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">qq0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E18">AS0</font></span></a>, <a class="ref" href="ndiff_5.html#T13" target="_self" title="NDIFF_5:th.13">MLT1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:22_1_1"/>
<font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1"><span class="lab"><font color="Green" title="E21">X1</font></span></a>, <a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E5:22"/><span class="lab"><font color="Green" title="E20">AS2</font></span>: 
 for <font color="Olive" title="b1">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">G</font> holds  <font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r0</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">qq0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span></span><br/><a NAME="E1:22_2"/>
 <a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1 is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></span>;<br/><a NAME="E2:22_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">X2</font></span>: 
<font color="Maroon" title="c7">qq0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E18">AS0</font></span></a>, <a class="ref" href="ndiff_5.html#T13" target="_self" title="NDIFF_5:th.13">MLT1</a></span>;<br/><a NAME="E3:22_2"/>
<font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22"><span class="lab"><font color="Green" title="E20">AS2</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E4:22_2"/>
<font color="Maroon" title="c4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">qq0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Maroon" title="c8">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_2"><span class="lab"><font color="Green" title="E21">X2</font></span></a>, <a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E7:22"/>
<font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E19">X0</font></span></a>, <a class="ref" href="ndiff_5.html#T12" target="_self" title="NDIFF_5:th.12">ADD1</a>, <a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E18">AS0</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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