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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">G3</font> be   <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font> &amp;  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> &amp;  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> &amp;  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:42"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">and </span><br/><a NAME="E2:42"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">and </span><br/><a NAME="E3:42"/><span class="lab"><font color="Green" title="E22">A3</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font>
 <span class="kw">and </span><br/><a NAME="E4:42"/><span class="lab"><font color="Green" title="E23">A4</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font>
 <span class="kw">and </span><br/><a NAME="E5:42"/><span class="lab"><font color="Green" title="E24">A5</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font>
 <span class="kw">and </span><br/><a NAME="E6:42"/><span class="lab"><font color="Green" title="E25">A6</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span><br/>

<a NAME="E7:42"/><span class="lab"><font color="Green" title="E26">A7</font></span>: 
 for <font color="Olive" title="b1">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font></span>)</span> holds <br/> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font></span>)</span> implies  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:42_1"/><span class="lab"><font color="Green" title="E27">A8</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/>

<a NAME="E2:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A9</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E3:42_1"/>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1"><span class="lab"><font color="Green" title="E27">A8</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E4:42_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 
;<br/>
<a NAME="E5:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A10</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E30">A11</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_1_1"/><span class="lab"><font color="Green" title="E31">A12</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E3:42_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A13</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42_1"><span class="lab"><font color="Green" title="E28">A9</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E1:42_1_1"><span class="lab"><font color="Green" title="E31">A12</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="txt" href="#E3:42_1_1"><span class="lab"><font color="Green" title="E32">A13</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_1_2"/><span class="lab"><font color="Green" title="E31">A14</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E3:42_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A15</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42_1"><span class="lab"><font color="Green" title="E28">A9</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E1:42_1_2"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E3:42_1_2"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</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="E8:42_1"/>
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42_1"><span class="lab"><font color="Green" title="E29">A10</font></span></a>, <a class="txt" href="#E6:42_1"><span class="lab"><font color="Green" title="E30">A11</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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>
<a NAME="E8:42"/><span class="lab"><font color="Green" title="E27">A16</font></span>: 
 for <font color="Olive" title="b1">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font></span>)</span> holds <br/> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font></span>)</span> implies  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:42_2"/><span class="lab"><font color="Green" title="E28">A17</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/>

<a NAME="E2:42_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A18</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E3:42_2"/>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_2"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E4:42_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 
;<br/>
<a NAME="E5:42_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A19</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E31">A20</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_2_1"/><span class="lab"><font color="Green" title="E32">A21</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E3:42_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A22</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42_2"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E1:42_2_1"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="txt" href="#E3:42_2_1"><span class="lab"><font color="Green" title="E33">A22</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_2_2"/><span class="lab"><font color="Green" title="E32">A23</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E3:42_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A24</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42_2"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E1:42_2_2"><span class="lab"><font color="Green" title="E32">A23</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E3:42_2_2"><span class="lab"><font color="Green" title="E33">A24</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</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="E8:42_2"/>
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42_2"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="txt" href="#E6:42_2"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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>
<a NAME="E9:42"/><span class="lab"><font color="Green" title="E28">A25</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:42"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E10:42"/><span class="lab"><font color="Green" title="E29">A26</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:42"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E11:42"/><span class="lab"><font color="Green" title="E30">A27</font></span>: 
 for <font color="Olive" title="b1">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> holds <br/> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> implies  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:42_3"/><span class="lab"><font color="Green" title="E31">A28</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/>

<a NAME="E2:42_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A29</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E3:42_3"/>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_3"><span class="lab"><font color="Green" title="E31">A28</font></span></a></span>;<br/>
<a NAME="E4:42_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/>
<a NAME="E5:42_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E6:42_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A30</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E34">A31</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_3_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_3_1"/><span class="lab"><font color="Green" title="E35">A32</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A33</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42_3"><span class="lab"><font color="Green" title="E32">A29</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E1:42_3_1"><span class="lab"><font color="Green" title="E35">A32</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42_3_1"><span class="lab"><font color="Green" title="E36">A33</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_3_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_3_2"/><span class="lab"><font color="Green" title="E35">A34</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A35</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42_3"><span class="lab"><font color="Green" title="E32">A29</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E1:42_3_2"><span class="lab"><font color="Green" title="E35">A34</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="txt" href="#E2:42_3_2"><span class="lab"><font color="Green" title="E36">A35</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</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="E9:42_3"/>
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:42_3"><span class="lab"><font color="Green" title="E33">A30</font></span></a>, <a class="txt" href="#E7:42_3"><span class="lab"><font color="Green" title="E34">A31</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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>
<a NAME="E12:42"/><span class="lab"><font color="Green" title="E31">A36</font></span>: 
 for <font color="Olive" title="b1">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> holds <br/> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> implies  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:42_4"/><span class="lab"><font color="Green" title="E32">A37</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/>

<a NAME="E2:42_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A38</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E3:42_4"/>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_4"><span class="lab"><font color="Green" title="E32">A37</font></span></a></span>;<br/>
<a NAME="E4:42_4"/><span class="kw">then </span>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/>
<a NAME="E5:42_4"/><span class="kw">then </span>
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E6:42_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A39</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E35">A40</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_4_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_4_1"/><span class="lab"><font color="Green" title="E36">A41</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_4_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A42</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42_4"><span class="lab"><font color="Green" title="E33">A38</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E1:42_4_1"><span class="lab"><font color="Green" title="E36">A41</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E2:42_4_1"><span class="lab"><font color="Green" title="E37">A42</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_4_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_4_2"/><span class="lab"><font color="Green" title="E36">A43</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_4_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A44</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42_4"><span class="lab"><font color="Green" title="E33">A38</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E1:42_4_2"><span class="lab"><font color="Green" title="E36">A43</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="txt" href="#E2:42_4_2"><span class="lab"><font color="Green" title="E37">A44</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</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="E9:42_4"/>
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:42_4"><span class="lab"><font color="Green" title="E34">A39</font></span></a>, <a class="txt" href="#E7:42_4"><span class="lab"><font color="Green" title="E35">A40</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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>
<a NAME="E13:42"/><span class="lab"><font color="Green" title="E32">A45</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:42"><span class="lab"><font color="Green" title="E30">A27</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<a NAME="E14:42"/><span class="lab"><font color="Green" title="E33">A46</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:42"><span class="lab"><font color="Green" title="E31">A36</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<span class="lab"><font color="Green" title="E34">A47</font></span>:  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> = 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></span>
<br/>.= 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:42"><span class="lab"><font color="Green" title="E32">A45</font></span></a>, <a class="txt" href="#E14:42"><span class="lab"><font color="Green" title="E33">A46</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
;<br/>
<span class="lab"><font color="Green" title="E35">A48</font></span>:  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> = 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">G3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">G3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">G3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></span>
<br/>.= 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:42"><span class="lab"><font color="Green" title="E32">A45</font></span></a>, <a class="txt" href="#E14:42"><span class="lab"><font color="Green" title="E33">A46</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
;<br/>
<span class="lab"><font color="Green" title="E36">A49</font></span>:  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> = 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:42"><span class="lab"><font color="Green" title="E34">A47</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
<br/>.= 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
;<br/>
<a NAME="E18:42"/>
 for <font color="Olive" title="b1">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> holds <br/> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> implies  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:42_8"/><span class="lab"><font color="Green" title="E37">A50</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/>

 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> = 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
<br/>.= 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
;<br/>
<a NAME="E3:42_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A51</font></span>: 
( <font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> or <font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_8"><span class="lab"><font color="Green" title="E37">A50</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E39">A52</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_8_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_8_2"/><span class="lab"><font color="Green" title="E40">A53</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_8_2"/>
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E3:42_8_2"/><span class="kw">then </span>
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/><span class="kw">hence </span> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="txt" href="#E1:42_8_2"><span class="lab"><font color="Green" title="E40">A53</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E1:42_8_2"><span class="lab"><font color="Green" title="E40">A53</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:42"><span class="lab"><font color="Green" title="E32">A45</font></span></a>, <a class="txt" href="#E14:42"><span class="lab"><font color="Green" title="E33">A46</font></span></a>, <a class="txt" href="#E1:42_8_2"><span class="lab"><font color="Green" title="E40">A53</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
;<br/> <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="lab"><font color="Green" title="E40">A54</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_8_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_8_3"/><span class="lab"><font color="Green" title="E41">A55</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_8_3"/>
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E3:42_8_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A56</font></span>: 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/><a NAME="E4:42_8_3"/>
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E5:42_8_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A57</font></span>: 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="txt" href="#E1:42_8_3"><span class="lab"><font color="Green" title="E41">A55</font></span></a>, <a class="txt" href="#E3:42_8_3"><span class="lab"><font color="Green" title="E42">A56</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">G2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E1:42_8_3"><span class="lab"><font color="Green" title="E41">A55</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E1:42_8_3"><span class="lab"><font color="Green" title="E41">A55</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:42"><span class="lab"><font color="Green" title="E32">A45</font></span></a>, <a class="txt" href="#E14:42"><span class="lab"><font color="Green" title="E33">A46</font></span></a>, <a class="txt" href="#E1:42_8_3"><span class="lab"><font color="Green" title="E41">A55</font></span></a>, <a class="txt" href="#E5:42_8_3"><span class="lab"><font color="Green" title="E43">A57</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_8_4"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_8_4"/><span class="lab"><font color="Green" title="E41">A58</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_8_4"/>
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E3:42_8_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A59</font></span>: 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="txt" href="#E1:42_8_4"><span class="lab"><font color="Green" title="E41">A58</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E1:42_8_4"><span class="lab"><font color="Green" title="E41">A58</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:42"><span class="lab"><font color="Green" title="E32">A45</font></span></a>, <a class="txt" href="#E14:42"><span class="lab"><font color="Green" title="E33">A46</font></span></a>, <a class="txt" href="#E1:42_8_4"><span class="lab"><font color="Green" title="E41">A58</font></span></a>, <a class="txt" href="#E3:42_8_4"><span class="lab"><font color="Green" title="E42">A59</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</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="E7:42_8"/>
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42_8"><span class="lab"><font color="Green" title="E38">A51</font></span></a>, <a class="txt" href="#E4:42_8"><span class="lab"><font color="Green" title="E39">A52</font></span></a>, <a class="txt" href="#E5:42_8"><span class="lab"><font color="Green" title="E40">A54</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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>
<a NAME="E19:42"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A60</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:42"><span class="lab"><font color="Green" title="E36">A49</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</a></span>;<br/>
<span class="lab"><font color="Green" title="E38">A61</font></span>:  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> = 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:42"><span class="lab"><font color="Green" title="E34">A47</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
<br/>.= 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
;<br/>
<a NAME="E21:42"/>
 for <font color="Olive" title="b1">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> holds <br/> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_10"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> implies  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:42_10"/><span class="lab"><font color="Green" title="E39">A62</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/>

 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> = 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>
<br/>.= 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
;<br/>
<a NAME="E3:42_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A63</font></span>: 
( <font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> or <font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_10"><span class="lab"><font color="Green" title="E39">A62</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E41">A64</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_10_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_10_2"/><span class="lab"><font color="Green" title="E42">A65</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_10_2"/>
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E3:42_10_2"/><span class="kw">then </span>
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/><span class="kw">hence </span> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="txt" href="#E1:42_10_2"><span class="lab"><font color="Green" title="E42">A65</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">G1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E1:42_10_2"><span class="lab"><font color="Green" title="E42">A65</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:42"><span class="lab"><font color="Green" title="E32">A45</font></span></a>, <a class="txt" href="#E14:42"><span class="lab"><font color="Green" title="E33">A46</font></span></a>, <a class="txt" href="#E1:42_10_2"><span class="lab"><font color="Green" title="E42">A65</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
;<br/> <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="lab"><font color="Green" title="E42">A66</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_10_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_10_3"/><span class="lab"><font color="Green" title="E43">A67</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_10_3"/>
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E3:42_10_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A68</font></span>: 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/><a NAME="E4:42_10_3"/>
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E5:42_10_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A69</font></span>: 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="txt" href="#E1:42_10_3"><span class="lab"><font color="Green" title="E43">A67</font></span></a>, <a class="txt" href="#E3:42_10_3"><span class="lab"><font color="Green" title="E44">A68</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">G2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E1:42_10_3"><span class="lab"><font color="Green" title="E43">A67</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E1:42_10_3"><span class="lab"><font color="Green" title="E43">A67</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:42"><span class="lab"><font color="Green" title="E32">A45</font></span></a>, <a class="txt" href="#E14:42"><span class="lab"><font color="Green" title="E33">A46</font></span></a>, <a class="txt" href="#E1:42_10_3"><span class="lab"><font color="Green" title="E43">A67</font></span></a>, <a class="txt" href="#E5:42_10_3"><span class="lab"><font color="Green" title="E45">A69</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_10_4"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_10_4"/><span class="lab"><font color="Green" title="E43">A70</font></span>: 
<font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font></span><br/><a NAME="E2:42_10_4"/>
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">G2</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E3:42_10_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A71</font></span>: 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">G3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>;<br/><span class="kw">thus </span> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> = 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">G3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="txt" href="#E1:42_10_4"><span class="lab"><font color="Green" title="E43">A70</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E1:42_10_4"><span class="lab"><font color="Green" title="E43">A70</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:42"><span class="lab"><font color="Green" title="E32">A45</font></span></a>, <a class="txt" href="#E14:42"><span class="lab"><font color="Green" title="E33">A46</font></span></a>, <a class="txt" href="#E1:42_10_4"><span class="lab"><font color="Green" title="E43">A70</font></span></a>, <a class="txt" href="#E3:42_10_4"><span class="lab"><font color="Green" title="E44">A71</font></span></a>, <a class="ref" href="graph_1.html#D3" target="_self" title="GRAPH_1:def.3">Def3</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="E7:42_10"/>
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42_10"><span class="lab"><font color="Green" title="E40">A63</font></span></a>, <a class="txt" href="#E4:42_10"><span class="lab"><font color="Green" title="E41">A64</font></span></a>, <a class="txt" href="#E5:42_10"><span class="lab"><font color="Green" title="E42">A66</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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="E22:42"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c2">G2</font></span>)</span> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="graph_1.html#K3" title="GRAPH_1:func.3">\/</a> <font color="Maroon" title="c3">G3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:42"><span class="lab"><font color="Green" title="E34">A47</font></span></a>, <a class="txt" href="#E16:42"><span class="lab"><font color="Green" title="E35">A48</font></span></a>, <a class="txt" href="#E19:42"><span class="lab"><font color="Green" title="E37">A60</font></span></a>, <a class="txt" href="#E20:42"><span class="lab"><font color="Green" title="E38">A61</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</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>
