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<span class="kw">let </span><font color="Maroon" title="c5">m</font>, <font color="Maroon" title="c6">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">n</font> implies <span class="p1">(<span class="default">3 <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c5">m</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">3 <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default">3 <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">3 <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:202"/><span class="lab"><font color="Green" title="E138">A1</font></span>: 
<font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">n</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">3 <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c5">m</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">3 <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default">3 <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">3 <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span><br/>

<a NAME="E2:202"/><span class="lab"><font color="Green" title="E139">A2</font></span>: 
3 <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 3 <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c6">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:202"><span class="lab"><font color="Green" title="E138">A1</font></span></a>, <a class="txt" href="number08.html#E169"><span class="lab"><font color="Green" title="E133">Lm57</font></span></a>, <a class="ref" href="nat_6.html#T2" onmouseover="rs('nat_6/T2')" onmouseout="rh()">NAT_6:2</a></span>;<br/>
<a NAME="E3:202"/>
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c6">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:202"><span class="lab"><font color="Green" title="E138">A1</font></span></a>, <a class="ref" href="xreal_1.html#T15" onmouseover="rs('xreal_1/T15')" onmouseout="rh()">XREAL_1:15</a></span>;<br/>
<a NAME="E4:202"/><span class="kw">then </span>
3 <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 3 <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">m</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T39" onmouseover="rs('power/T39')" onmouseout="rh()">POWER:39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:202"/>
<span class="p1">(<span class="default">3 <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c5">m</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">3 <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">m</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default">3 <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">3 <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:202"><span class="lab"><font color="Green" title="E139">A2</font></span></a>, <a class="ref" href="xreal_1.html#T14" onmouseover="rs('xreal_1/T14')" onmouseout="rh()">XREAL_1:14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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