Step |
Hyp |
Ref |
Expression |
1 |
|
3nn0 |
|
2 |
|
1nn0 |
|
3 |
1 2
|
deccl |
|
4 |
|
7nn |
|
5 |
3 4
|
decnncl |
|
6 |
|
8nn0 |
|
7 |
|
4nn0 |
|
8 |
|
7nn0 |
|
9 |
|
3lt8 |
|
10 |
|
1lt10 |
|
11 |
|
7lt10 |
|
12 |
1 6 2 7 8 2 9 10 11
|
3decltc |
|
13 |
|
1nn |
|
14 |
1 13
|
decnncl |
|
15 |
14 8 2 10
|
declti |
|
16 |
|
3t2e6 |
|
17 |
|
df-7 |
|
18 |
3 1 16 17
|
dec2dvds |
|
19 |
|
3nn |
|
20 |
|
10nn0 |
|
21 |
|
5nn0 |
|
22 |
20 21
|
deccl |
|
23 |
|
2nn |
|
24 |
|
0nn0 |
|
25 |
|
2nn0 |
|
26 |
|
eqid |
|
27 |
25
|
dec0h |
|
28 |
|
eqid |
|
29 |
|
ax-1cn |
|
30 |
29
|
addid2i |
|
31 |
2
|
dec0h |
|
32 |
30 31
|
eqtri |
|
33 |
|
3cn |
|
34 |
33
|
mulid1i |
|
35 |
|
00id |
|
36 |
34 35
|
oveq12i |
|
37 |
33
|
addid1i |
|
38 |
36 37
|
eqtri |
|
39 |
33
|
mul01i |
|
40 |
39
|
oveq1i |
|
41 |
40 30
|
eqtri |
|
42 |
41 31
|
eqtri |
|
43 |
2 24 24 2 28 32 1 2 24 38 42
|
decma2c |
|
44 |
|
5cn |
|
45 |
|
5t3e15 |
|
46 |
44 33 45
|
mulcomli |
|
47 |
|
5p2e7 |
|
48 |
2 21 25 46 47
|
decaddi |
|
49 |
20 21 24 25 26 27 1 8 2 43 48
|
decma2c |
|
50 |
|
2lt3 |
|
51 |
19 22 23 49 50
|
ndvdsi |
|
52 |
|
2lt5 |
|
53 |
3 23 52 47
|
dec5dvds2 |
|
54 |
7 21
|
deccl |
|
55 |
|
eqid |
|
56 |
33
|
addid2i |
|
57 |
56
|
oveq2i |
|
58 |
|
7t4e28 |
|
59 |
|
2p1e3 |
|
60 |
|
8p3e11 |
|
61 |
25 6 1 58 59 2 60
|
decaddci |
|
62 |
57 61
|
eqtri |
|
63 |
|
7t5e35 |
|
64 |
1 21 25 63 47
|
decaddi |
|
65 |
7 21 24 25 55 27 8 8 1 62 64
|
decma2c |
|
66 |
|
2lt7 |
|
67 |
4 54 23 65 66
|
ndvdsi |
|
68 |
2 13
|
decnncl |
|
69 |
25 6
|
deccl |
|
70 |
|
9nn |
|
71 |
|
9nn0 |
|
72 |
|
eqid |
|
73 |
71
|
dec0h |
|
74 |
2 2
|
deccl |
|
75 |
|
eqid |
|
76 |
|
9cn |
|
77 |
76
|
addid2i |
|
78 |
77 73
|
eqtri |
|
79 |
|
2cn |
|
80 |
79
|
mulid2i |
|
81 |
80 30
|
oveq12i |
|
82 |
81 59
|
eqtri |
|
83 |
80
|
oveq1i |
|
84 |
|
9p2e11 |
|
85 |
76 79 84
|
addcomli |
|
86 |
83 85
|
eqtri |
|
87 |
2 2 24 71 75 78 25 2 2 82 86
|
decmac |
|
88 |
|
8cn |
|
89 |
88
|
mulid2i |
|
90 |
89 30
|
oveq12i |
|
91 |
|
8p1e9 |
|
92 |
90 91
|
eqtri |
|
93 |
89
|
oveq1i |
|
94 |
|
9p8e17 |
|
95 |
76 88 94
|
addcomli |
|
96 |
93 95
|
eqtri |
|
97 |
2 2 24 71 75 73 6 8 2 92 96
|
decmac |
|
98 |
25 6 24 71 72 73 74 8 71 87 97
|
decma2c |
|
99 |
|
9lt10 |
|
100 |
13 2 71 99
|
declti |
|
101 |
68 69 70 98 100
|
ndvdsi |
|
102 |
2 19
|
decnncl |
|
103 |
25 7
|
deccl |
|
104 |
|
5nn |
|
105 |
|
eqid |
|
106 |
21
|
dec0h |
|
107 |
2 1
|
deccl |
|
108 |
|
eqid |
|
109 |
44
|
addid2i |
|
110 |
109 106
|
eqtri |
|
111 |
16
|
oveq1i |
|
112 |
|
6p5e11 |
|
113 |
111 112
|
eqtri |
|
114 |
2 1 24 21 108 110 25 2 2 82 113
|
decmac |
|
115 |
|
4cn |
|
116 |
115
|
mulid2i |
|
117 |
116 30
|
oveq12i |
|
118 |
|
4p1e5 |
|
119 |
117 118
|
eqtri |
|
120 |
|
4t3e12 |
|
121 |
115 33 120
|
mulcomli |
|
122 |
44 79 47
|
addcomli |
|
123 |
2 25 21 121 122
|
decaddi |
|
124 |
2 1 24 21 108 106 7 8 2 119 123
|
decmac |
|
125 |
25 7 24 21 105 106 107 8 21 114 124
|
decma2c |
|
126 |
|
5lt10 |
|
127 |
13 1 21 126
|
declti |
|
128 |
102 103 104 125 127
|
ndvdsi |
|
129 |
2 4
|
decnncl |
|
130 |
2 6
|
deccl |
|
131 |
|
eqid |
|
132 |
2 8
|
deccl |
|
133 |
|
eqid |
|
134 |
|
3p1e4 |
|
135 |
33 29 134
|
addcomli |
|
136 |
24 2 2 1 31 108 30 135
|
decadd |
|
137 |
29
|
mulid1i |
|
138 |
|
1p1e2 |
|
139 |
137 138
|
oveq12i |
|
140 |
|
1p2e3 |
|
141 |
139 140
|
eqtri |
|
142 |
|
7cn |
|
143 |
142
|
mulid1i |
|
144 |
143
|
oveq1i |
|
145 |
|
7p4e11 |
|
146 |
144 145
|
eqtri |
|
147 |
2 8 2 7 133 136 2 2 2 141 146
|
decmac |
|
148 |
89 109
|
oveq12i |
|
149 |
|
8p5e13 |
|
150 |
148 149
|
eqtri |
|
151 |
|
6nn0 |
|
152 |
|
6p1e7 |
|
153 |
|
8t7e56 |
|
154 |
88 142 153
|
mulcomli |
|
155 |
21 151 152 154
|
decsuc |
|
156 |
2 8 24 2 133 31 6 8 21 150 155
|
decmac |
|
157 |
2 6 2 2 131 75 132 8 107 147 156
|
decma2c |
|
158 |
|
1lt7 |
|
159 |
2 2 4 158
|
declt |
|
160 |
129 130 68 157 159
|
ndvdsi |
|
161 |
2 70
|
decnncl |
|
162 |
2 151
|
deccl |
|
163 |
|
eqid |
|
164 |
2 71
|
deccl |
|
165 |
|
eqid |
|
166 |
24 2 2 2 31 75 30 138
|
decadd |
|
167 |
76
|
mulid1i |
|
168 |
167
|
oveq1i |
|
169 |
168 84
|
eqtri |
|
170 |
2 71 2 25 165 166 2 2 2 141 169
|
decmac |
|
171 |
1
|
dec0h |
|
172 |
|
6cn |
|
173 |
172
|
mulid2i |
|
174 |
173 109
|
oveq12i |
|
175 |
174 112
|
eqtri |
|
176 |
|
9t6e54 |
|
177 |
|
4p3e7 |
|
178 |
21 7 1 176 177
|
decaddi |
|
179 |
2 71 24 1 165 171 151 8 21 175 178
|
decmac |
|
180 |
2 151 2 1 163 108 164 8 74 170 179
|
decma2c |
|
181 |
|
3lt9 |
|
182 |
2 1 70 181
|
declt |
|
183 |
161 162 102 180 182
|
ndvdsi |
|
184 |
25 19
|
decnncl |
|
185 |
102
|
nnnn0i |
|
186 |
|
8nn |
|
187 |
2 186
|
decnncl |
|
188 |
25 1
|
deccl |
|
189 |
|
eqid |
|
190 |
|
7p1e8 |
|
191 |
142 29 190
|
addcomli |
|
192 |
6
|
dec0h |
|
193 |
191 192
|
eqtri |
|
194 |
79
|
mulid1i |
|
195 |
194 30
|
oveq12i |
|
196 |
195 59
|
eqtri |
|
197 |
34
|
oveq1i |
|
198 |
88 33 60
|
addcomli |
|
199 |
197 198
|
eqtri |
|
200 |
25 1 24 6 189 193 2 2 2 196 199
|
decmac |
|
201 |
33 79 16
|
mulcomli |
|
202 |
201 30
|
oveq12i |
|
203 |
202 152
|
eqtri |
|
204 |
|
3t3e9 |
|
205 |
204
|
oveq1i |
|
206 |
205 94
|
eqtri |
|
207 |
25 1 24 6 189 192 1 8 2 203 206
|
decmac |
|
208 |
2 1 2 6 108 131 188 8 8 200 207
|
decma2c |
|
209 |
|
8lt10 |
|
210 |
|
1lt2 |
|
211 |
2 25 6 1 209 210
|
decltc |
|
212 |
184 185 187 208 211
|
ndvdsi |
|
213 |
5 12 15 18 51 53 67 101 128 160 183 212
|
prmlem2 |
|