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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">m</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <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">  for <font color="Olive" title="b1">z1</font>, <font color="Olive" title="b2">z2</font> being   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of <font color="Maroon" title="c1">m</font>, <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> <br/>  for <font color="Olive" title="b3">d1</font>, <font color="Olive" title="b4">d2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>  holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b3">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Olive" title="b2">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b4">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b3">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Olive" title="b2">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b4">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b3">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b2">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b4">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b3">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b4">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">z1</font>, <font color="Maroon" title="c3">z2</font> be   <a href="finseq_2.html#NM3" title="FINSEQ_2:NM.3">Tuple</a> of <font color="Maroon" title="c1">m</font>, <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">d1</font>, <font color="Olive" title="b2">d2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>  holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">d1</font>, <font color="Maroon" title="c5">d2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c6">f</font> =  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">t</font> =  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> ;<br/>
<a NAME="E1:17"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
 <a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">set </span><font color="Maroon" title="c8">siki1</font> =  <a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <font color="Maroon" title="c3">z2</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">siki2</font> =  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>);<br/>
<a NAME="E1:17_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <font color="Maroon" title="c3">z2</font></span>)</span>
 
;<br/>
<span class="kw">hence </span><a NAME="E2:17_1"/>
 <a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T21" onmouseover="rs('binarith/T21')" onmouseout="rh()">BINARITH:21</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/>


</div><span class="kw">end;</span></div>
<span class="lab"><font color="Green" title="E13">A2</font></span>:  <a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> = 
 <a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c5">d2</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p4">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span></span>)</span></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T19" onmouseover="rs('binarith/T19')" onmouseout="rh()">BINARITH:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c5">d2</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="binari_2.html#T10" target="_self" onmouseover="rs('binari_2/T10')" onmouseout="rh()">Th10</a></span>
;<br/>
<span class="lab"><font color="Green" title="E14">A3</font></span>:  <a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>) = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c4">d1</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c4">d1</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">d2</font></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c4">d1</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">d2</font></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T18" onmouseover="rs('binarith/T18')" onmouseout="rh()">BINARITH:18</a></span>
;<br/>
<span class="lab"><font color="Green" title="E15">A4</font></span>:  <a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c5">d2</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K4" title="BINARITH:func.4">carry</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T2" onmouseover="rs('binarith/T2')" onmouseout="rh()">BINARITH:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c5">d2</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T18" onmouseover="rs('binarith/T18')" onmouseout="rh()">BINARITH:18</a></span>
;<br/>
<a NAME="E5:17"/><span class="lab"><font color="Green" title="E16">A5</font></span>: 
 <a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<font color="Maroon" title="c4">d1</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T10" target="_self" onmouseover="rs('binari_2/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<a NAME="E6:17"/><span class="lab"><font color="Green" title="E17">A6</font></span>: 
 <a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p2"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<font color="Maroon" title="c5">d2</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="binari_2.html#T10" target="_self" onmouseover="rs('binari_2/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:17_5"/>
( ( <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  &amp; <font color="Maroon" title="c5">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  ) or ( <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  &amp; <font color="Maroon" title="c5">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  ) or ( <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  &amp; <font color="Maroon" title="c5">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  ) or ( <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  &amp; <font color="Maroon" title="c5">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  ) )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_1"><span class="kw">suppose </span></a><a NAME="E1:17_5_1"/><span class="lab"><font color="Green" title="E18">A7</font></span>: 
( <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  &amp; <font color="Maroon" title="c5">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A8</font></span>: <span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<font color="Maroon" title="c4">d1</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>
<br/>.= 
 <a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font>

;<br/><span class="lab"><font color="Green" title="E20">A9</font></span>: <span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<font color="Maroon" title="c5">d2</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17_5_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>
<br/>.= 
 <a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font>

;<br/><a NAME="E4:17_5_1"/><span class="lab"><font color="Green" title="E21">A10</font></span>: 
 <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">d1</font> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <font color="Maroon" title="c5">d2</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span></span>)</span></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17_5_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>;<br/><span class="kw">thus </span><a NAME="E5:17_5_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</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><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_5_1_3"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_1_3_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:17_5_1_3_1"/>
(  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  or  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_1_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:17_5_1_3_1_1"/>
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:17_5_1_3_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E1:17_5_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E2:17_5_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="binari_2.html#T10" target="_self" onmouseover="rs('binari_2/T10')" onmouseout="rh()">Th10</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_1_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:17_5_1_3_1_2"/><span class="lab"><font color="Green" title="E22">A11</font></span>: 
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:17_5_1_3_1_2"/><span class="kw">then </span>
 <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E1:17_5_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E4:17_5_1"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E1:17_5_1_3_1_2"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T25" onmouseover="rs('power/T25')" onmouseout="rh()">POWER:25</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T27" onmouseover="rs('power/T27')" onmouseout="rh()">POWER:27</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span>

;<br/><span class="kw">hence </span><a NAME="E4:17_5_1_3_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E2:17_5_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E3:17_5_1"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="binari_2.html#T10" target="_self" onmouseover="rs('binari_2/T10')" onmouseout="rh()">Th10</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_2"><span class="kw">suppose </span></a><a NAME="E1:17_5_2"/><span class="lab"><font color="Green" title="E18">A12</font></span>: 
( <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  &amp; <font color="Maroon" title="c5">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A13</font></span>: <span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<font color="Maroon" title="c5">d2</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>
<br/>.= 
 <a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font>

;<br/><span class="kw">thus </span><a NAME="E3:17_5_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</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><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_5_2_2"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_2_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:17_5_2_2_1"/>
(  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  or  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_2_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:17_5_2_2_1_1"/><span class="lab"><font color="Green" title="E20">A14</font></span>: 
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:17_5_2_2_1_1"/><span class="kw">then </span>
 <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>;<br/><span class="kw">hence </span><a NAME="E3:17_5_2_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E1:17_5_2"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E2:17_5_2"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E1:17_5_2_2_1_1"><span class="lab"><font color="Green" title="E20">A14</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_2_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:17_5_2_2_1_2"/>
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:17_5_2_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E1:17_5_2"><span class="lab"><font color="Green" title="E18">A12</font></span></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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_3"><span class="kw">suppose </span></a><a NAME="E1:17_5_3"/><span class="lab"><font color="Green" title="E18">A15</font></span>: 
( <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  &amp; <font color="Maroon" title="c5">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A16</font></span>: <span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<font color="Maroon" title="c4">d1</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>
<br/>.= 
 <a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font>

;<br/><span class="kw">thus </span><a NAME="E3:17_5_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</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><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_5_3_2"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_3_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:17_5_3_2_1"/>
(  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  or  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_3_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:17_5_3_2_1_1"/><span class="lab"><font color="Green" title="E20">A17</font></span>: 
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:17_5_3_2_1_1"/><span class="kw">then </span>
 <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>;<br/><span class="kw">hence </span><a NAME="E3:17_5_3_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E1:17_5_3"><span class="lab"><font color="Green" title="E18">A15</font></span></a>, <a class="txt" href="#E2:17_5_3"><span class="lab"><font color="Green" title="E19">A16</font></span></a>, <a class="txt" href="#E1:17_5_3_2_1_1"><span class="lab"><font color="Green" title="E20">A17</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_3_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:17_5_3_2_1_2"/>
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:17_5_3_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E1:17_5_3"><span class="lab"><font color="Green" title="E18">A15</font></span></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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_4"><span class="kw">suppose </span></a><a NAME="E1:17_5_4"/><span class="lab"><font color="Green" title="E18">A18</font></span>: 
( <font color="Maroon" title="c4">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  &amp; <font color="Maroon" title="c5">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:17_5_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A19</font></span>: 
<span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<font color="Maroon" title="c5">d2</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>;<br/><span class="lab"><font color="Green" title="E20">A20</font></span>: <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<font color="Maroon" title="c4">d1</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E16">A5</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E1:17_5_4"><span class="lab"><font color="Green" title="E18">A18</font></span></a>, <a class="txt" href="#E2:17_5_4"><span class="lab"><font color="Green" title="E19">A19</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T25" onmouseover="rs('power/T25')" onmouseout="rh()">POWER:25</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T27" onmouseover="rs('power/T27')" onmouseout="rh()">POWER:27</a></span>
;<br/><a NAME="E4:17_5_4"/><span class="lab"><font color="Green" title="E21">A21</font></span>: 
 <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c4">d1</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <font color="Maroon" title="c5">d2</font></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span></span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17_5_4"><span class="lab"><font color="Green" title="E18">A18</font></span></a>, <a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>;<br/><span class="kw">thus </span><a NAME="E5:17_5_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</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><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_5_4_2"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_4_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:17_5_4_2_1"/>
(  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  or  <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_4_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:17_5_4_2_1_1"/><span class="lab"><font color="Green" title="E22">A22</font></span>: 
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:17_5_4_2_1_1"/><span class="kw">then </span>
 <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>;<br/><span class="kw">hence </span><a NAME="E3:17_5_4_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E1:17_5_4"><span class="lab"><font color="Green" title="E18">A18</font></span></a>, <a class="txt" href="#E3:17_5_4"><span class="lab"><font color="Green" title="E20">A20</font></span></a>, <a class="txt" href="#E4:17_5_4"><span class="lab"><font color="Green" title="E21">A21</font></span></a>, <a class="txt" href="#E1:17_5_4_2_1_1"><span class="lab"><font color="Green" title="E22">A22</font></span></a>, <a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_5_4_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:17_5_4_2_1_2"/><span class="lab"><font color="Green" title="E22">A23</font></span>: 
 <a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:17_5_4_2_1_2"/><span class="kw">then </span>
 <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p1">(<span class="default"><a href="binarith.html#K8" title="BINARITH:func.8">add_ovfl</a> (<font color="Maroon" title="c2">z1</font>,<font color="Maroon" title="c3">z2</font>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#D8" onmouseover="rs('funcop_1/D8')" onmouseout="rh()">FUNCOP_1:def 8</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E1:17_5_4"><span class="lab"><font color="Green" title="E18">A18</font></span></a>, <a class="txt" href="#E1:17_5_4_2_1_2"><span class="lab"><font color="Green" title="E22">A23</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Maroon" title="c1">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T25" onmouseover="rs('power/T25')" onmouseout="rh()">POWER:25</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><a href="binarith.html#K6" title="BINARITH:func.6">Absval</a> <font color="Maroon" title="c3">z2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T27" onmouseover="rs('power/T27')" onmouseout="rh()">POWER:27</a></span>
;<br/><span class="kw">hence </span><a NAME="E4:17_5_4_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span> <a href="binarith.html#K7" title="BINARITH:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p3">(<span class="default"><a href="binari_2.html#K4" title="BINARI_2:func.4">Int_add_ovfl</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p5"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="funcop_1.html#K16" title="FUNCOP_1:func.16">IFEQ</a> (<span class="p2">(<span class="default"><a href="binari_2.html#K5" title="BINARI_2:func.5">Int_add_udfl</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p4"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span>)</span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d1</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="binari_2.html#K3" title="BINARI_2:func.3">Intval</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z2</font> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p3"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c5">d2</font></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17_5_4"><span class="lab"><font color="Green" title="E20">A20</font></span></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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
