Step |
Hyp |
Ref |
Expression |
1 |
|
1nn0 |
|
2 |
|
2nn0 |
|
3 |
1 2
|
deccl |
|
4 |
|
7nn |
|
5 |
3 4
|
decnncl |
|
6 |
|
8nn0 |
|
7 |
|
4nn0 |
|
8 |
|
7nn0 |
|
9 |
|
1lt8 |
|
10 |
|
2lt10 |
|
11 |
|
7lt10 |
|
12 |
1 6 2 7 8 1 9 10 11
|
3decltc |
|
13 |
|
2nn |
|
14 |
1 13
|
decnncl |
|
15 |
|
1lt10 |
|
16 |
14 8 1 15
|
declti |
|
17 |
|
3nn0 |
|
18 |
|
3t2e6 |
|
19 |
|
df-7 |
|
20 |
3 17 18 19
|
dec2dvds |
|
21 |
|
3nn |
|
22 |
|
1nn |
|
23 |
|
3t3e9 |
|
24 |
23
|
oveq1i |
|
25 |
|
9p1e10 |
|
26 |
24 25
|
eqtri |
|
27 |
|
1lt3 |
|
28 |
21 17 22 26 27
|
ndvdsi |
|
29 |
1 2 8
|
3dvds2dec |
|
30 |
|
1p2e3 |
|
31 |
30
|
oveq1i |
|
32 |
|
7cn |
|
33 |
|
3cn |
|
34 |
|
7p3e10 |
|
35 |
32 33 34
|
addcomli |
|
36 |
31 35
|
eqtri |
|
37 |
36
|
breq2i |
|
38 |
29 37
|
bitri |
|
39 |
28 38
|
mtbir |
|
40 |
|
2lt5 |
|
41 |
|
5p2e7 |
|
42 |
3 13 40 41
|
dec5dvds2 |
|
43 |
1 6
|
deccl |
|
44 |
|
0nn0 |
|
45 |
|
eqid |
|
46 |
1
|
dec0h |
|
47 |
|
5nn0 |
|
48 |
32
|
mulid1i |
|
49 |
|
5cn |
|
50 |
49
|
addid2i |
|
51 |
48 50
|
oveq12i |
|
52 |
|
7p5e12 |
|
53 |
51 52
|
eqtri |
|
54 |
|
6nn0 |
|
55 |
|
8cn |
|
56 |
|
8t7e56 |
|
57 |
55 32 56
|
mulcomli |
|
58 |
|
6p1e7 |
|
59 |
47 54 1 57 58
|
decaddi |
|
60 |
1 6 44 1 45 46 8 8 47 53 59
|
decma2c |
|
61 |
|
1lt7 |
|
62 |
4 43 22 60 61
|
ndvdsi |
|
63 |
1 22
|
decnncl |
|
64 |
1 1
|
deccl |
|
65 |
|
6nn |
|
66 |
|
eqid |
|
67 |
54
|
dec0h |
|
68 |
64
|
nn0cni |
|
69 |
68
|
mulid1i |
|
70 |
|
ax-1cn |
|
71 |
70
|
addid2i |
|
72 |
69 71
|
oveq12i |
|
73 |
|
1p1e2 |
|
74 |
1 1 1 66 73
|
decaddi |
|
75 |
72 74
|
eqtri |
|
76 |
|
6cn |
|
77 |
76 70 58
|
addcomli |
|
78 |
1 1 54 69 77
|
decaddi |
|
79 |
1 1 44 54 66 67 64 8 1 75 78
|
decma2c |
|
80 |
|
6lt10 |
|
81 |
22 1 54 80
|
declti |
|
82 |
63 64 65 79 81
|
ndvdsi |
|
83 |
1 21
|
decnncl |
|
84 |
|
9nn0 |
|
85 |
|
10nn |
|
86 |
|
eqid |
|
87 |
|
eqid |
|
88 |
|
9cn |
|
89 |
88
|
mulid2i |
|
90 |
89 30
|
oveq12i |
|
91 |
|
9p3e12 |
|
92 |
90 91
|
eqtri |
|
93 |
|
9t3e27 |
|
94 |
88 33 93
|
mulcomli |
|
95 |
32
|
addid1i |
|
96 |
2 8 44 94 95
|
decaddi |
|
97 |
1 17 1 44 86 87 84 8 2 92 96
|
decmac |
|
98 |
|
3pos |
|
99 |
1 44 21 98
|
declt |
|
100 |
83 84 85 97 99
|
ndvdsi |
|
101 |
1 4
|
decnncl |
|
102 |
|
8nn |
|
103 |
|
eqid |
|
104 |
32
|
mulid2i |
|
105 |
104
|
oveq1i |
|
106 |
105 52
|
eqtri |
|
107 |
|
7t7e49 |
|
108 |
|
4p1e5 |
|
109 |
|
9p8e17 |
|
110 |
7 84 6 107 108 8 109
|
decaddci |
|
111 |
1 8 6 103 8 8 47 106 110
|
decrmac |
|
112 |
|
8lt10 |
|
113 |
22 8 6 112
|
declti |
|
114 |
101 8 102 111 113
|
ndvdsi |
|
115 |
|
9nn |
|
116 |
1 115
|
decnncl |
|
117 |
|
eqid |
|
118 |
76
|
mulid2i |
|
119 |
|
5p1e6 |
|
120 |
49 70 119
|
addcomli |
|
121 |
118 120
|
oveq12i |
|
122 |
|
6p6e12 |
|
123 |
121 122
|
eqtri |
|
124 |
|
9t6e54 |
|
125 |
|
4p3e7 |
|
126 |
47 7 17 124 125
|
decaddi |
|
127 |
1 84 1 17 117 86 54 8 47 123 126
|
decmac |
|
128 |
|
3lt9 |
|
129 |
1 17 115 128
|
declt |
|
130 |
116 54 83 127 129
|
ndvdsi |
|
131 |
2 21
|
decnncl |
|
132 |
|
eqid |
|
133 |
|
eqid |
|
134 |
|
2cn |
|
135 |
|
5t2e10 |
|
136 |
49 134 135
|
mulcomli |
|
137 |
136 73
|
oveq12i |
|
138 |
|
dec10p |
|
139 |
137 138
|
eqtri |
|
140 |
|
5t3e15 |
|
141 |
49 33 140
|
mulcomli |
|
142 |
1 47 2 141 41
|
decaddi |
|
143 |
2 17 1 2 132 133 47 8 1 139 142
|
decmac |
|
144 |
|
1lt2 |
|
145 |
1 2 2 17 10 144
|
decltc |
|
146 |
131 47 14 143 145
|
ndvdsi |
|
147 |
5 12 16 20 39 42 62 82 100 114 130 146
|
prmlem2 |
|