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<a NAME="E1:69"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="descip_1.html#K25" title="DESCIP_1:func.25">DES-PIP</a> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="descip_1.html#K27" title="DESCIP_1:func.27">DES-PIPINV</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 64 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E2:69"/>
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 64 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> holds <br/><span class="p1">(<span class="default"><a href="descip_1.html#K25" title="DESCIP_1:func.25">DES-PIP</a> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="descip_1.html#K27" title="DESCIP_1:func.27">DES-PIPINV</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="69_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">x</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="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 64 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> implies <span class="p1">(<span class="default"><a href="descip_1.html#K25" title="DESCIP_1:func.25">DES-PIP</a> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="descip_1.html#K27" title="DESCIP_1:func.27">DES-PIPINV</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:69_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 64 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</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="descip_1.html#K25" title="DESCIP_1:func.25">DES-PIP</a> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="descip_1.html#K27" title="DESCIP_1:func.27">DES-PIPINV</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">x</font> = <font color="Maroon" title="c1">x</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of 64 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> ;<br/>
<span class="p1">(<span class="default"><a href="descip_1.html#K25" title="DESCIP_1:func.25">DES-PIP</a> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="descip_1.html#K27" title="DESCIP_1:func.27">DES-PIPINV</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> = 
<a href="descip_1.html#K25" title="DESCIP_1:func.25">DES-PIP</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="descip_1.html#K27" title="DESCIP_1:func.27">DES-PIPINV</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" onmouseover="rs('funct_2/T15')" onmouseout="rh()">FUNCT_2:15</a></span>
<br/>.= 
<a href="descip_1.html#K25" title="DESCIP_1:func.25">DES-PIP</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="descip_1.html#K26" title="DESCIP_1:func.26">DES-IPINV</a> <font color="Maroon" title="c2">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="descip_1.html#D17" target="_self" onmouseover="rs('descip_1/D17')" onmouseout="rh()">Def17</a></span>
<br/>.= 
 <a href="descip_1.html#K24" title="DESCIP_1:func.24">DES-IP</a> <span class="p1">(<span class="default"><a href="descip_1.html#K26" title="DESCIP_1:func.26">DES-IPINV</a> <font color="Maroon" title="c2">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="descip_1.html#D15" target="_self" onmouseover="rs('descip_1/D15')" onmouseout="rh()">Def15</a></span>
<br/>.= 
<font color="Maroon" title="c2">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="descip_1.html#E50"><span class="lab"><font color="Green" title="E31">Lm6</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:69_1"/>
<span class="p1">(<span class="default"><a href="descip_1.html#K25" title="DESCIP_1:func.25">DES-PIP</a> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="descip_1.html#K27" title="DESCIP_1:func.27">DES-PIPINV</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</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>
<span class="kw">hence </span><a NAME="E3:69"/>
<a href="descip_1.html#K25" title="DESCIP_1:func.25">DES-PIP</a> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="descip_1.html#K27" title="DESCIP_1:func.27">DES-PIPINV</a> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default">64 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="funct_1.html#T17" onmouseover="rs('funct_1/T17')" onmouseout="rh()">FUNCT_1:17</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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