Step |
Hyp |
Ref |
Expression |
1 |
|
finxpreclem4.1 |
|
2 |
|
2onn |
|
3 |
|
nnon |
|
4 |
|
2on |
|
5 |
|
oawordeu |
|
6 |
4 5
|
mpanl1 |
|
7 |
|
riotasbc |
|
8 |
6 7
|
syl |
|
9 |
|
riotaex |
|
10 |
|
sbceq1g |
|
11 |
9 10
|
ax-mp |
|
12 |
|
csbov2g |
|
13 |
9 12
|
ax-mp |
|
14 |
9
|
csbvargi |
|
15 |
14
|
oveq2i |
|
16 |
13 15
|
eqtri |
|
17 |
16
|
eqeq1i |
|
18 |
11 17
|
bitri |
|
19 |
8 18
|
sylib |
|
20 |
3 19
|
sylan |
|
21 |
|
simpl |
|
22 |
20 21
|
eqeltrd |
|
23 |
|
riotacl |
|
24 |
|
riotaund |
|
25 |
|
0elon |
|
26 |
24 25
|
eqeltrdi |
|
27 |
23 26
|
pm2.61i |
|
28 |
|
nnarcl |
|
29 |
4 28
|
mpan |
|
30 |
2
|
biantrur |
|
31 |
29 30
|
bitr4di |
|
32 |
27 31
|
ax-mp |
|
33 |
22 32
|
sylib |
|
34 |
|
nnacom |
|
35 |
2 33 34
|
sylancr |
|
36 |
|
df-2o |
|
37 |
36
|
oveq2i |
|
38 |
|
1onn |
|
39 |
|
nnasuc |
|
40 |
33 38 39
|
sylancl |
|
41 |
37 40
|
syl5eq |
|
42 |
35 20 41
|
3eqtr3d |
|
43 |
3
|
adantr |
|
44 |
|
sucidg |
|
45 |
38 44
|
ax-mp |
|
46 |
45 36
|
eleqtrri |
|
47 |
|
ssel |
|
48 |
46 47
|
mpi |
|
49 |
48
|
ne0d |
|
50 |
49
|
adantl |
|
51 |
|
nnlim |
|
52 |
51
|
adantr |
|
53 |
|
onsucuni3 |
|
54 |
43 50 52 53
|
syl3anc |
|
55 |
|
nnacom |
|
56 |
33 38 55
|
sylancl |
|
57 |
|
suceq |
|
58 |
56 57
|
syl |
|
59 |
42 54 58
|
3eqtr3d |
|
60 |
|
ordom |
|
61 |
|
ordelss |
|
62 |
60 61
|
mpan |
|
63 |
|
nnfi |
|
64 |
|
nnunifi |
|
65 |
62 63 64
|
syl2anc |
|
66 |
65
|
adantr |
|
67 |
|
nnacl |
|
68 |
38 33 67
|
sylancr |
|
69 |
|
peano4 |
|
70 |
66 68 69
|
syl2anc |
|
71 |
59 70
|
mpbid |
|
72 |
71
|
fveq2d |
|
73 |
72
|
adantr |
|
74 |
33
|
adantr |
|
75 |
|
df-1o |
|
76 |
75
|
fveq2i |
|
77 |
|
rdgsuc |
|
78 |
25 77
|
ax-mp |
|
79 |
|
opex |
|
80 |
79
|
rdg0 |
|
81 |
80
|
fveq2i |
|
82 |
76 78 81
|
3eqtri |
|
83 |
1
|
finxpreclem3 |
|
84 |
82 83
|
eqtr4id |
|
85 |
84
|
fveq2d |
|
86 |
|
2on0 |
|
87 |
|
nnlim |
|
88 |
2 87
|
ax-mp |
|
89 |
|
rdgsucuni |
|
90 |
4 86 88 89
|
mp3an |
|
91 |
|
1oequni2o |
|
92 |
91
|
fveq2i |
|
93 |
92
|
fveq2i |
|
94 |
90 93
|
eqtr4i |
|
95 |
75
|
fveq2i |
|
96 |
|
rdgsuc |
|
97 |
25 96
|
ax-mp |
|
98 |
|
opex |
|
99 |
98
|
rdg0 |
|
100 |
99
|
fveq2i |
|
101 |
95 97 100
|
3eqtri |
|
102 |
85 94 101
|
3eqtr4g |
|
103 |
|
1on |
|
104 |
|
rdgeqoa |
|
105 |
4 103 104
|
mp3an12 |
|
106 |
74 102 105
|
sylc |
|
107 |
20
|
fveq2d |
|
108 |
107
|
adantr |
|
109 |
73 106 108
|
3eqtr2rd |
|