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<b>let </b><font color="Maroon" title="c1">m</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">m</font> holds <br/><span class="p1">(<span class="default"><a href="idea_1.html#K13" title="IDEA_1:func.13">IDEAoperationC</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2</span><br/><b>let </b><font color="Maroon" title="c2">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">m</font> implies <span class="p1">(<span class="default"><a href="idea_1.html#K13" title="IDEA_1:func.13">IDEAoperationC</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 )</span><br/>



<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E35">A1</font></i>: 
( <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Maroon" title="c2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">m</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="idea_1.html#K13" title="IDEA_1:func.13">IDEAoperationC</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2</span><br/>

<b>then </b><span class="p1">(<span class="default"><a href="idea_1.html#K13" title="IDEA_1:func.13">IDEAoperationC</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">i</font> = 
 <a href="funcop_1.html#K15" title="FUNCOP_1:func.15">IFEQ</a> <font color="Maroon" title="c2">i</font>,2,<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="funcop_1.html#K15" title="FUNCOP_1:func.15">IFEQ</a> <font color="Maroon" title="c2">i</font>,3,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="idea_1.html#D13" target="_self" title="IDEA_1:def.13">Def13</a></i>
<br/>.= 
 <a href="funcop_1.html#K15" title="FUNCOP_1:func.15">IFEQ</a> <font color="Maroon" title="c2">i</font>,3,<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">i</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:43"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2
<b>by </b><i><a class="txt" href="#E1:43"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="funcop_1.html#D8" title="FUNCOP_1:def.8">FUNCOP_1:def 8</a></i>
;<br/>
<b>hence </b><a NAME="E3:43"/>
<span class="p1">(<span class="default"><a href="idea_1.html#K13" title="IDEA_1:func.13">IDEAoperationC</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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