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<div><span class="lab"><font color="Green" title="E7">A1</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="11_1_1_1"><span class="kw">now </span> <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">p</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  holds <br/><span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> (<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">x</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c2">n</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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"> ( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  implies <span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> (<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">x</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c2">n</font> )</span><br/><span class="kw">assume </span><a NAME="E1:11_1_1_1"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</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"> <span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> (<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">x</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c2">n</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">r</font> = <font color="Maroon" title="c5">p</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/><a NAME="E3:11_1_1_1"/><span class="lab"><font color="Green" title="E8">A2</font></span>: 
<span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> (<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">x</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> (<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c6">r</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pdiff_1.html#D5" target="_self" onmouseover="rs('pdiff_1/D5')" onmouseout="rh()">Def5</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">IT</font> = <span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> (<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">x</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">r</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/> <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">IT</font> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:11_1_1_1"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="finseq_7.html#T5" onmouseover="rs('finseq_7/T5')" onmouseout="rh()">FINSEQ_7:5</a></span>
<br/>.= 
<font color="Maroon" title="c2">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" onmouseover="rs('card_1/D7')" onmouseout="rh()">CARD_1:def 7</a></span>
;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">IT</font> = <font color="Maroon" title="c7">IT</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T92" onmouseover="rs('finseq_2/T92')" onmouseout="rh()">FINSEQ_2:92</a></span>;<br/><a NAME="E7:11_1_1_1"/>
<font color="Maroon" title="c8">IT</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c2">n</font>
 ;<br/><span class="kw">hence </span><a NAME="E8:11_1_1_1"/>
<span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> (<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">x</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c2">n</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"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E2:11_1_1"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> (<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pdiff_1.html#D5" target="_self" onmouseover="rs('pdiff_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:11_1_1"/>
 <a href="pdiff_1.html#K5" title="PDIFF_1:func.5">reproj</a> (<font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">x</font>) is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11_1_1"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="funct_2.html#T3" onmouseover="rs('funct_2/T3')" onmouseout="rh()">FUNCT_2:3</a></span>; <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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