Step |
Hyp |
Ref |
Expression |
1 |
|
sqrtcvallem5 |
|
2 |
1
|
recnd |
|
3 |
|
ax-icn |
|
4 |
3
|
a1i |
|
5 |
|
neg1rr |
|
6 |
|
1re |
|
7 |
5 6
|
ifcli |
|
8 |
7
|
a1i |
|
9 |
|
sqrtcvallem3 |
|
10 |
8 9
|
remulcld |
|
11 |
10
|
recnd |
|
12 |
4 11
|
mulcld |
|
13 |
2 12
|
addcld |
|
14 |
|
id |
|
15 |
|
binom2 |
|
16 |
2 12 15
|
syl2anc |
|
17 |
|
abscl |
|
18 |
|
recl |
|
19 |
17 18
|
readdcld |
|
20 |
19
|
rehalfcld |
|
21 |
20
|
recnd |
|
22 |
21
|
sqsqrtd |
|
23 |
4 11
|
sqmuld |
|
24 |
|
i2 |
|
25 |
24
|
a1i |
|
26 |
8
|
recnd |
|
27 |
9
|
recnd |
|
28 |
26 27
|
sqmuld |
|
29 |
|
ovif |
|
30 |
|
neg1sqe1 |
|
31 |
|
sq1 |
|
32 |
|
ifeq12 |
|
33 |
30 31 32
|
mp2an |
|
34 |
|
ifid |
|
35 |
29 33 34
|
3eqtri |
|
36 |
35
|
a1i |
|
37 |
17 18
|
resubcld |
|
38 |
37
|
rehalfcld |
|
39 |
38
|
recnd |
|
40 |
39
|
sqsqrtd |
|
41 |
36 40
|
oveq12d |
|
42 |
39
|
mulid2d |
|
43 |
28 41 42
|
3eqtrd |
|
44 |
25 43
|
oveq12d |
|
45 |
39
|
mulm1d |
|
46 |
23 44 45
|
3eqtrd |
|
47 |
22 46
|
oveq12d |
|
48 |
21 39
|
negsubd |
|
49 |
17
|
recnd |
|
50 |
18
|
recnd |
|
51 |
49 50 50
|
pnncand |
|
52 |
50
|
2timesd |
|
53 |
51 52
|
eqtr4d |
|
54 |
53
|
oveq1d |
|
55 |
19
|
recnd |
|
56 |
37
|
recnd |
|
57 |
|
2cnd |
|
58 |
|
2ne0 |
|
59 |
58
|
a1i |
|
60 |
55 56 57 59
|
divsubdird |
|
61 |
50 57 59
|
divcan3d |
|
62 |
54 60 61
|
3eqtr3d |
|
63 |
47 48 62
|
3eqtrd |
|
64 |
57 2
|
mulcld |
|
65 |
64 4 11
|
mul12d |
|
66 |
57 2 12
|
mulassd |
|
67 |
57 2 11
|
mulassd |
|
68 |
2 26 27
|
mul12d |
|
69 |
|
sqrtcvallem4 |
|
70 |
|
halfnneg2 |
|
71 |
19 70
|
syl |
|
72 |
69 71
|
mpbird |
|
73 |
|
2rp |
|
74 |
73
|
a1i |
|
75 |
19 72 74
|
sqrtdivd |
|
76 |
|
sqrtcvallem2 |
|
77 |
|
halfnneg2 |
|
78 |
37 77
|
syl |
|
79 |
76 78
|
mpbird |
|
80 |
37 79 74
|
sqrtdivd |
|
81 |
75 80
|
oveq12d |
|
82 |
19 72
|
resqrtcld |
|
83 |
82
|
recnd |
|
84 |
|
2re |
|
85 |
84
|
a1i |
|
86 |
|
0le2 |
|
87 |
86
|
a1i |
|
88 |
85 87
|
resqrtcld |
|
89 |
88
|
recnd |
|
90 |
37 79
|
resqrtcld |
|
91 |
90
|
recnd |
|
92 |
|
sqrt00 |
|
93 |
84 86 92
|
mp2an |
|
94 |
93
|
necon3bii |
|
95 |
58 94
|
mpbir |
|
96 |
95
|
a1i |
|
97 |
83 89 91 89 96 96
|
divmuldivd |
|
98 |
18
|
resqcld |
|
99 |
98
|
recnd |
|
100 |
|
imcl |
|
101 |
100
|
resqcld |
|
102 |
101
|
recnd |
|
103 |
|
absvalsq2 |
|
104 |
99 102 103
|
mvrladdd |
|
105 |
|
subsq |
|
106 |
49 50 105
|
syl2anc |
|
107 |
104 106
|
eqtr3d |
|
108 |
107
|
fveq2d |
|
109 |
100
|
absred |
|
110 |
|
reabsifneg |
|
111 |
100 110
|
syl |
|
112 |
109 111
|
eqtr3d |
|
113 |
19 72 37 79
|
sqrtmuld |
|
114 |
108 112 113
|
3eqtr3rd |
|
115 |
|
remsqsqrt |
|
116 |
84 86 115
|
mp2an |
|
117 |
116
|
a1i |
|
118 |
114 117
|
oveq12d |
|
119 |
81 97 118
|
3eqtrd |
|
120 |
119
|
oveq2d |
|
121 |
68 120
|
eqtrd |
|
122 |
121
|
oveq2d |
|
123 |
100
|
renegcld |
|
124 |
123 100
|
ifcld |
|
125 |
124
|
recnd |
|
126 |
26 125 57 59
|
divassd |
|
127 |
|
ovif12 |
|
128 |
5
|
a1i |
|
129 |
128
|
recnd |
|
130 |
100
|
recnd |
|
131 |
129 129 130
|
mulassd |
|
132 |
|
neg1mulneg1e1 |
|
133 |
132
|
a1i |
|
134 |
133
|
oveq1d |
|
135 |
130
|
mulid2d |
|
136 |
134 135
|
eqtrd |
|
137 |
130
|
mulm1d |
|
138 |
137
|
oveq2d |
|
139 |
131 136 138
|
3eqtr3rd |
|
140 |
139
|
adantr |
|
141 |
135
|
adantr |
|
142 |
140 141
|
ifeqda |
|
143 |
127 142
|
syl5eq |
|
144 |
143
|
oveq1d |
|
145 |
126 144
|
eqtr3d |
|
146 |
145
|
oveq2d |
|
147 |
130 57 59
|
divcan2d |
|
148 |
146 147
|
eqtrd |
|
149 |
67 122 148
|
3eqtrd |
|
150 |
149
|
oveq2d |
|
151 |
65 66 150
|
3eqtr3d |
|
152 |
63 151
|
oveq12d |
|
153 |
1
|
resqcld |
|
154 |
153
|
recnd |
|
155 |
2 12
|
mulcld |
|
156 |
57 155
|
mulcld |
|
157 |
12
|
sqcld |
|
158 |
154 156 157
|
add32d |
|
159 |
|
replim |
|
160 |
152 158 159
|
3eqtr4d |
|
161 |
16 160
|
eqtrd |
|
162 |
20 69
|
sqrtge0d |
|
163 |
1 10
|
crred |
|
164 |
162 163
|
breqtrrd |
|
165 |
|
reim |
|
166 |
13 165
|
syl |
|
167 |
166 163
|
eqtr3d |
|
168 |
167
|
eqeq1d |
|
169 |
|
cnsqrt00 |
|
170 |
21 169
|
syl |
|
171 |
|
half0 |
|
172 |
55 171
|
syl |
|
173 |
49 50
|
addcomd |
|
174 |
173
|
eqeq1d |
|
175 |
|
addeq0 |
|
176 |
50 49 175
|
syl2anc |
|
177 |
172 174 176
|
3bitrd |
|
178 |
168 170 177
|
3bitrd |
|
179 |
|
olc |
|
180 |
|
eqcom |
|
181 |
180
|
a1i |
|
182 |
|
sqeqor |
|
183 |
50 49 182
|
syl2anc |
|
184 |
103
|
eqeq1d |
|
185 |
|
addid0 |
|
186 |
99 102 185
|
syl2anc |
|
187 |
|
sqeq0 |
|
188 |
130 187
|
syl |
|
189 |
184 186 188
|
3bitrd |
|
190 |
181 183 189
|
3bitr3d |
|
191 |
179 190
|
syl5ib |
|
192 |
191
|
ancld |
|
193 |
178 192
|
sylbid |
|
194 |
|
simp2 |
|
195 |
194
|
oveq2d |
|
196 |
|
simp1 |
|
197 |
196 49
|
syl |
|
198 |
197
|
negidd |
|
199 |
195 198
|
eqtrd |
|
200 |
199
|
oveq1d |
|
201 |
|
2cn |
|
202 |
201 58
|
div0i |
|
203 |
200 202
|
eqtrdi |
|
204 |
203
|
fveq2d |
|
205 |
|
sqrt0 |
|
206 |
204 205
|
eqtrdi |
|
207 |
|
simp3 |
|
208 |
|
0red |
|
209 |
208
|
ltnrd |
|
210 |
207 209
|
eqnbrtrd |
|
211 |
210
|
iffalsed |
|
212 |
194
|
oveq2d |
|
213 |
49 49
|
subnegd |
|
214 |
49
|
2timesd |
|
215 |
213 214
|
eqtr4d |
|
216 |
196 215
|
syl |
|
217 |
212 216
|
eqtrd |
|
218 |
217
|
oveq1d |
|
219 |
49 57 59
|
divcan3d |
|
220 |
196 219
|
syl |
|
221 |
218 220
|
eqtrd |
|
222 |
221
|
fveq2d |
|
223 |
211 222
|
oveq12d |
|
224 |
|
absge0 |
|
225 |
17 224
|
resqrtcld |
|
226 |
225
|
recnd |
|
227 |
226
|
mulid2d |
|
228 |
196 227
|
syl |
|
229 |
223 228
|
eqtrd |
|
230 |
229
|
oveq2d |
|
231 |
206 230
|
oveq12d |
|
232 |
4 226
|
mulcld |
|
233 |
196 232
|
syl |
|
234 |
233
|
addid2d |
|
235 |
231 234
|
eqtrd |
|
236 |
235
|
oveq2d |
|
237 |
|
ixi |
|
238 |
237
|
a1i |
|
239 |
238
|
oveq1d |
|
240 |
4 4 226
|
mulassd |
|
241 |
226
|
mulm1d |
|
242 |
239 240 241
|
3eqtr3d |
|
243 |
196 242
|
syl |
|
244 |
236 243
|
eqtrd |
|
245 |
244
|
fveq2d |
|
246 |
225
|
renegcld |
|
247 |
246
|
rered |
|
248 |
196 247
|
syl |
|
249 |
245 248
|
eqtrd |
|
250 |
17 224
|
sqrtge0d |
|
251 |
225
|
le0neg2d |
|
252 |
250 251
|
mpbid |
|
253 |
196 252
|
syl |
|
254 |
249 253
|
eqbrtrd |
|
255 |
254
|
3expib |
|
256 |
193 255
|
syld |
|
257 |
4 13
|
mulcld |
|
258 |
257
|
sqrtcvallem1 |
|
259 |
256 258
|
mpbid |
|
260 |
13 14 161 164 259
|
eqsqrtd |
|
261 |
260
|
eqcomd |
|