Step |
Hyp |
Ref |
Expression |
1 |
|
hgt750lemg.f |
|
2 |
|
hgt750lemg.t |
|
3 |
|
hgt750lemg.n |
|
4 |
|
hgt750lemg.l |
|
5 |
|
hgt750lemg.1 |
|
6 |
|
2fveq3 |
|
7 |
|
tpfi |
|
8 |
7
|
a1i |
|
9 |
|
fzo0to3tp |
|
10 |
|
f1oeq23 |
|
11 |
9 9 10
|
mp2an |
|
12 |
2 11
|
sylib |
|
13 |
|
eqidd |
|
14 |
4
|
adantr |
|
15 |
3
|
adantr |
|
16 |
|
simpr |
|
17 |
16 9
|
eleqtrrdi |
|
18 |
15 17
|
ffvelrnd |
|
19 |
14 18
|
ffvelrnd |
|
20 |
19
|
recnd |
|
21 |
6 8 12 13 20
|
fprodf1o |
|
22 |
1
|
a1i |
|
23 |
|
simpr |
|
24 |
23
|
coeq1d |
|
25 |
|
f1of |
|
26 |
2 25
|
syl |
|
27 |
|
ovexd |
|
28 |
|
fex2 |
|
29 |
26 27 27 28
|
syl3anc |
|
30 |
|
coexg |
|
31 |
5 29 30
|
syl2anc |
|
32 |
22 24 5 31
|
fvmptd |
|
33 |
32
|
adantr |
|
34 |
33
|
fveq1d |
|
35 |
|
f1ofun |
|
36 |
2 35
|
syl |
|
37 |
36
|
adantr |
|
38 |
|
f1odm |
|
39 |
12 38
|
syl |
|
40 |
39
|
eleq2d |
|
41 |
40
|
biimpar |
|
42 |
|
fvco |
|
43 |
37 41 42
|
syl2anc |
|
44 |
34 43
|
eqtr2d |
|
45 |
44
|
fveq2d |
|
46 |
45
|
prodeq2dv |
|
47 |
21 46
|
eqtr2d |
|
48 |
|
2fveq3 |
|
49 |
|
2fveq3 |
|
50 |
|
c0ex |
|
51 |
50
|
a1i |
|
52 |
|
1ex |
|
53 |
52
|
a1i |
|
54 |
32
|
fveq1d |
|
55 |
50
|
tpid1 |
|
56 |
55 39
|
eleqtrrid |
|
57 |
|
fvco |
|
58 |
36 56 57
|
syl2anc |
|
59 |
54 58
|
eqtrd |
|
60 |
55 9
|
eleqtrri |
|
61 |
60
|
a1i |
|
62 |
26 61
|
ffvelrnd |
|
63 |
3 62
|
ffvelrnd |
|
64 |
59 63
|
eqeltrd |
|
65 |
4 64
|
ffvelrnd |
|
66 |
65
|
recnd |
|
67 |
32
|
fveq1d |
|
68 |
52
|
tpid2 |
|
69 |
68 39
|
eleqtrrid |
|
70 |
|
fvco |
|
71 |
36 69 70
|
syl2anc |
|
72 |
67 71
|
eqtrd |
|
73 |
68 9
|
eleqtrri |
|
74 |
73
|
a1i |
|
75 |
26 74
|
ffvelrnd |
|
76 |
3 75
|
ffvelrnd |
|
77 |
72 76
|
eqeltrd |
|
78 |
4 77
|
ffvelrnd |
|
79 |
78
|
recnd |
|
80 |
|
0ne1 |
|
81 |
80
|
a1i |
|
82 |
|
2fveq3 |
|
83 |
|
2ex |
|
84 |
83
|
a1i |
|
85 |
32
|
fveq1d |
|
86 |
83
|
tpid3 |
|
87 |
86 39
|
eleqtrrid |
|
88 |
|
fvco |
|
89 |
36 87 88
|
syl2anc |
|
90 |
85 89
|
eqtrd |
|
91 |
86 9
|
eleqtrri |
|
92 |
91
|
a1i |
|
93 |
26 92
|
ffvelrnd |
|
94 |
3 93
|
ffvelrnd |
|
95 |
90 94
|
eqeltrd |
|
96 |
4 95
|
ffvelrnd |
|
97 |
96
|
recnd |
|
98 |
|
0ne2 |
|
99 |
98
|
a1i |
|
100 |
|
1ne2 |
|
101 |
100
|
a1i |
|
102 |
48 49 51 53 66 79 81 82 84 97 99 101
|
prodtp |
|
103 |
|
2fveq3 |
|
104 |
|
2fveq3 |
|
105 |
3 61
|
ffvelrnd |
|
106 |
4 105
|
ffvelrnd |
|
107 |
106
|
recnd |
|
108 |
3 74
|
ffvelrnd |
|
109 |
4 108
|
ffvelrnd |
|
110 |
109
|
recnd |
|
111 |
|
2fveq3 |
|
112 |
3 92
|
ffvelrnd |
|
113 |
4 112
|
ffvelrnd |
|
114 |
113
|
recnd |
|
115 |
103 104 51 53 107 110 81 111 84 114 99 101
|
prodtp |
|
116 |
47 102 115
|
3eqtr3d |
|
117 |
66 79 97
|
mulassd |
|
118 |
107 110 114
|
mulassd |
|
119 |
116 117 118
|
3eqtr3d |
|