Step |
Hyp |
Ref |
Expression |
1 |
|
iccpartgtprec.m |
|
2 |
|
iccpartgtprec.p |
|
3 |
|
ral0 |
|
4 |
|
oveq2 |
|
5 |
|
fzo0 |
|
6 |
4 5
|
eqtrdi |
|
7 |
6
|
raleqdv |
|
8 |
3 7
|
mpbiri |
|
9 |
8
|
a1d |
|
10 |
1
|
nnnn0d |
|
11 |
|
0elfz |
|
12 |
10 11
|
syl |
|
13 |
1 2 12
|
iccpartxr |
|
14 |
13
|
adantr |
|
15 |
|
elxr |
|
16 |
|
0zd |
|
17 |
|
elfzouz |
|
18 |
|
0p1e1 |
|
19 |
18
|
fveq2i |
|
20 |
17 19
|
eleqtrrdi |
|
21 |
20
|
adantl |
|
22 |
|
fveq2 |
|
23 |
22
|
eqcomd |
|
24 |
23
|
eleq1d |
|
25 |
24
|
biimpcd |
|
26 |
25
|
ad3antrrr |
|
27 |
1
|
adantr |
|
28 |
2
|
adantr |
|
29 |
|
elfz2nn0 |
|
30 |
|
elfzo2 |
|
31 |
|
simpl1 |
|
32 |
|
simpr2 |
|
33 |
|
nn0ge0 |
|
34 |
|
0red |
|
35 |
|
eluzelre |
|
36 |
35
|
adantr |
|
37 |
|
zre |
|
38 |
37
|
adantl |
|
39 |
|
lelttr |
|
40 |
34 36 38 39
|
syl3anc |
|
41 |
40
|
expcomd |
|
42 |
41
|
3impia |
|
43 |
33 42
|
syl5com |
|
44 |
43
|
3ad2ant2 |
|
45 |
44
|
imp |
|
46 |
|
elnnz |
|
47 |
32 45 46
|
sylanbrc |
|
48 |
|
nn0re |
|
49 |
48
|
ad2antrl |
|
50 |
|
nn0re |
|
51 |
50
|
adantl |
|
52 |
51
|
adantl |
|
53 |
38
|
adantr |
|
54 |
|
lelttr |
|
55 |
54
|
expd |
|
56 |
49 52 53 55
|
syl3anc |
|
57 |
56
|
exp31 |
|
58 |
57
|
com34 |
|
59 |
58
|
com35 |
|
60 |
59
|
3imp |
|
61 |
60
|
expdcom |
|
62 |
61
|
com34 |
|
63 |
62
|
3imp1 |
|
64 |
|
elfzo0 |
|
65 |
31 47 63 64
|
syl3anbrc |
|
66 |
65
|
ex |
|
67 |
30 66
|
syl5bi |
|
68 |
29 67
|
sylbi |
|
69 |
68
|
adantr |
|
70 |
69
|
impcom |
|
71 |
|
simpr |
|
72 |
71
|
adantl |
|
73 |
|
fzo1fzo0n0 |
|
74 |
70 72 73
|
sylanbrc |
|
75 |
74
|
adantl |
|
76 |
27 28 75
|
iccpartipre |
|
77 |
76
|
exp32 |
|
78 |
77
|
ad2antrl |
|
79 |
78
|
imp |
|
80 |
79
|
expdimp |
|
81 |
26 80
|
pm2.61dne |
|
82 |
1
|
adantr |
|
83 |
82
|
ad3antlr |
|
84 |
2
|
adantr |
|
85 |
84
|
ad3antlr |
|
86 |
|
elfzoelz |
|
87 |
86
|
adantl |
|
88 |
|
fzoval |
|
89 |
88
|
eqcomd |
|
90 |
87 89
|
syl |
|
91 |
90
|
eleq2d |
|
92 |
|
elfzouz2 |
|
93 |
92
|
adantl |
|
94 |
|
fzoss2 |
|
95 |
93 94
|
syl |
|
96 |
95
|
sseld |
|
97 |
91 96
|
sylbid |
|
98 |
97
|
imp |
|
99 |
|
iccpartimp |
|
100 |
83 85 98 99
|
syl3anc |
|
101 |
100
|
simprd |
|
102 |
16 21 81 101
|
smonoord |
|
103 |
102
|
ralrimiva |
|
104 |
103
|
ex |
|
105 |
|
lbfzo0 |
|
106 |
1 105
|
sylibr |
|
107 |
1 2 106
|
3jca |
|
108 |
107
|
ad2antrl |
|
109 |
108
|
adantr |
|
110 |
|
iccpartimp |
|
111 |
109 110
|
syl |
|
112 |
111
|
simprd |
|
113 |
|
breq1 |
|
114 |
113
|
adantr |
|
115 |
114
|
adantr |
|
116 |
112 115
|
mpbid |
|
117 |
1
|
ad2antrl |
|
118 |
117
|
adantr |
|
119 |
2
|
ad2antrl |
|
120 |
119
|
adantr |
|
121 |
|
1nn0 |
|
122 |
121
|
a1i |
|
123 |
|
nnnn0 |
|
124 |
|
nnge1 |
|
125 |
122 123 124
|
3jca |
|
126 |
1 125
|
syl |
|
127 |
|
elfz2nn0 |
|
128 |
126 127
|
sylibr |
|
129 |
18 128
|
eqeltrid |
|
130 |
129
|
ad2antrl |
|
131 |
130
|
adantr |
|
132 |
118 120 131
|
iccpartxr |
|
133 |
|
pnfnlt |
|
134 |
132 133
|
syl |
|
135 |
116 134
|
pm2.21dd |
|
136 |
135
|
ralrimiva |
|
137 |
136
|
ex |
|
138 |
1
|
adantr |
|
139 |
2
|
adantr |
|
140 |
|
simpr |
|
141 |
138 139 140
|
iccpartipre |
|
142 |
|
mnflt |
|
143 |
141 142
|
syl |
|
144 |
143
|
ralrimiva |
|
145 |
144
|
ad2antrl |
|
146 |
|
breq1 |
|
147 |
146
|
adantr |
|
148 |
147
|
ralbidv |
|
149 |
145 148
|
mpbird |
|
150 |
149
|
ex |
|
151 |
104 137 150
|
3jaoi |
|
152 |
15 151
|
sylbi |
|
153 |
14 152
|
mpcom |
|
154 |
153
|
expcom |
|
155 |
9 154
|
pm2.61i |
|