Step |
Hyp |
Ref |
Expression |
1 |
|
4sq.1 |
|
2 |
|
4sq.2 |
|
3 |
|
4sq.3 |
|
4 |
|
4sq.4 |
|
5 |
|
4sq.5 |
|
6 |
|
4sq.6 |
|
7 |
|
4sq.7 |
|
8 |
|
4sq.m |
|
9 |
|
4sq.a |
|
10 |
|
4sq.b |
|
11 |
|
4sq.c |
|
12 |
|
4sq.d |
|
13 |
|
4sq.e |
|
14 |
|
4sq.f |
|
15 |
|
4sq.g |
|
16 |
|
4sq.h |
|
17 |
|
4sq.r |
|
18 |
|
4sq.p |
|
19 |
|
eluz2nn |
|
20 |
8 19
|
syl |
|
21 |
9 20 13
|
4sqlem5 |
|
22 |
21
|
simpld |
|
23 |
|
zsqcl |
|
24 |
22 23
|
syl |
|
25 |
24
|
zred |
|
26 |
10 20 14
|
4sqlem5 |
|
27 |
26
|
simpld |
|
28 |
|
zsqcl |
|
29 |
27 28
|
syl |
|
30 |
29
|
zred |
|
31 |
25 30
|
readdcld |
|
32 |
11 20 15
|
4sqlem5 |
|
33 |
32
|
simpld |
|
34 |
|
zsqcl |
|
35 |
33 34
|
syl |
|
36 |
35
|
zred |
|
37 |
12 20 16
|
4sqlem5 |
|
38 |
37
|
simpld |
|
39 |
|
zsqcl |
|
40 |
38 39
|
syl |
|
41 |
40
|
zred |
|
42 |
36 41
|
readdcld |
|
43 |
20
|
nnred |
|
44 |
43
|
resqcld |
|
45 |
44
|
rehalfcld |
|
46 |
45
|
rehalfcld |
|
47 |
9 20 13
|
4sqlem7 |
|
48 |
10 20 14
|
4sqlem7 |
|
49 |
25 30 46 46 47 48
|
le2addd |
|
50 |
45
|
recnd |
|
51 |
50
|
2halvesd |
|
52 |
49 51
|
breqtrd |
|
53 |
11 20 15
|
4sqlem7 |
|
54 |
12 20 16
|
4sqlem7 |
|
55 |
36 41 46 46 53 54
|
le2addd |
|
56 |
55 51
|
breqtrd |
|
57 |
31 42 45 45 52 56
|
le2addd |
|
58 |
44
|
recnd |
|
59 |
58
|
2halvesd |
|
60 |
57 59
|
breqtrd |
|
61 |
43
|
recnd |
|
62 |
61
|
sqvald |
|
63 |
60 62
|
breqtrd |
|
64 |
31 42
|
readdcld |
|
65 |
20
|
nngt0d |
|
66 |
|
ledivmul |
|
67 |
64 43 43 65 66
|
syl112anc |
|
68 |
63 67
|
mpbird |
|
69 |
17 68
|
eqbrtrid |
|
70 |
|
simpr |
|
71 |
17 70
|
syl5eqr |
|
72 |
64
|
recnd |
|
73 |
20
|
nnne0d |
|
74 |
72 61 73
|
diveq0ad |
|
75 |
|
zsqcl2 |
|
76 |
22 75
|
syl |
|
77 |
|
zsqcl2 |
|
78 |
27 77
|
syl |
|
79 |
76 78
|
nn0addcld |
|
80 |
79
|
nn0ge0d |
|
81 |
|
zsqcl2 |
|
82 |
33 81
|
syl |
|
83 |
|
zsqcl2 |
|
84 |
38 83
|
syl |
|
85 |
82 84
|
nn0addcld |
|
86 |
85
|
nn0ge0d |
|
87 |
|
add20 |
|
88 |
31 80 42 86 87
|
syl22anc |
|
89 |
74 88
|
bitrd |
|
90 |
89
|
biimpa |
|
91 |
71 90
|
syldan |
|
92 |
91
|
simpld |
|
93 |
76
|
nn0ge0d |
|
94 |
78
|
nn0ge0d |
|
95 |
|
add20 |
|
96 |
25 93 30 94 95
|
syl22anc |
|
97 |
96
|
biimpa |
|
98 |
92 97
|
syldan |
|
99 |
98
|
simpld |
|
100 |
9 20 13 99
|
4sqlem9 |
|
101 |
98
|
simprd |
|
102 |
10 20 14 101
|
4sqlem9 |
|
103 |
20
|
nnsqcld |
|
104 |
103
|
nnzd |
|
105 |
|
zsqcl |
|
106 |
9 105
|
syl |
|
107 |
|
zsqcl |
|
108 |
10 107
|
syl |
|
109 |
|
dvds2add |
|
110 |
104 106 108 109
|
syl3anc |
|
111 |
110
|
adantr |
|
112 |
100 102 111
|
mp2and |
|
113 |
91
|
simprd |
|
114 |
82
|
nn0ge0d |
|
115 |
84
|
nn0ge0d |
|
116 |
|
add20 |
|
117 |
36 114 41 115 116
|
syl22anc |
|
118 |
117
|
biimpa |
|
119 |
113 118
|
syldan |
|
120 |
119
|
simpld |
|
121 |
11 20 15 120
|
4sqlem9 |
|
122 |
119
|
simprd |
|
123 |
12 20 16 122
|
4sqlem9 |
|
124 |
|
zsqcl |
|
125 |
11 124
|
syl |
|
126 |
|
zsqcl |
|
127 |
12 126
|
syl |
|
128 |
|
dvds2add |
|
129 |
104 125 127 128
|
syl3anc |
|
130 |
129
|
adantr |
|
131 |
121 123 130
|
mp2and |
|
132 |
106 108
|
zaddcld |
|
133 |
125 127
|
zaddcld |
|
134 |
|
dvds2add |
|
135 |
104 132 133 134
|
syl3anc |
|
136 |
135
|
adantr |
|
137 |
112 131 136
|
mp2and |
|
138 |
104
|
adantr |
|
139 |
132
|
adantr |
|
140 |
51
|
adantr |
|
141 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
|
4sqlem15 |
|
142 |
141
|
simpld |
|
143 |
142
|
simpld |
|
144 |
46
|
recnd |
|
145 |
24
|
zcnd |
|
146 |
144 145
|
subeq0ad |
|
147 |
146
|
adantr |
|
148 |
143 147
|
mpbid |
|
149 |
24
|
adantr |
|
150 |
148 149
|
eqeltrd |
|
151 |
150 150
|
zaddcld |
|
152 |
140 151
|
eqeltrrd |
|
153 |
139 152
|
zsubcld |
|
154 |
133
|
adantr |
|
155 |
154 152
|
zsubcld |
|
156 |
106
|
adantr |
|
157 |
156 150
|
zsubcld |
|
158 |
108
|
adantr |
|
159 |
158 150
|
zsubcld |
|
160 |
9 20 13 143
|
4sqlem10 |
|
161 |
142
|
simprd |
|
162 |
10 20 14 161
|
4sqlem10 |
|
163 |
138 157 159 160 162
|
dvds2addd |
|
164 |
106
|
zcnd |
|
165 |
108
|
zcnd |
|
166 |
164 165 144 144
|
addsub4d |
|
167 |
51
|
oveq2d |
|
168 |
166 167
|
eqtr3d |
|
169 |
168
|
adantr |
|
170 |
163 169
|
breqtrd |
|
171 |
125
|
adantr |
|
172 |
171 150
|
zsubcld |
|
173 |
127
|
adantr |
|
174 |
173 150
|
zsubcld |
|
175 |
141
|
simprd |
|
176 |
175
|
simpld |
|
177 |
11 20 15 176
|
4sqlem10 |
|
178 |
175
|
simprd |
|
179 |
12 20 16 178
|
4sqlem10 |
|
180 |
138 172 174 177 179
|
dvds2addd |
|
181 |
125
|
zcnd |
|
182 |
127
|
zcnd |
|
183 |
181 182 144 144
|
addsub4d |
|
184 |
51
|
oveq2d |
|
185 |
183 184
|
eqtr3d |
|
186 |
185
|
adantr |
|
187 |
180 186
|
breqtrd |
|
188 |
138 153 155 170 187
|
dvds2addd |
|
189 |
132
|
zcnd |
|
190 |
133
|
zcnd |
|
191 |
189 190 50 50
|
addsub4d |
|
192 |
59
|
oveq2d |
|
193 |
191 192
|
eqtr3d |
|
194 |
193
|
adantr |
|
195 |
188 194
|
breqtrd |
|
196 |
132 133
|
zaddcld |
|
197 |
196
|
adantr |
|
198 |
|
dvdssubr |
|
199 |
138 197 198
|
syl2anc |
|
200 |
195 199
|
mpbird |
|
201 |
137 200
|
jaodan |
|
202 |
18
|
adantr |
|
203 |
201 202
|
breqtrrd |
|
204 |
203
|
ex |
|
205 |
69 204
|
jca |
|