Step |
Hyp |
Ref |
Expression |
1 |
|
lincsum.p |
|
2 |
|
lincsum.x |
|
3 |
|
lincsum.y |
|
4 |
|
lincsum.s |
|
5 |
|
lincsum.r |
|
6 |
|
lincsum.b |
|
7 |
|
eqid |
|
8 |
|
eqid |
|
9 |
|
lmodcmn |
|
10 |
9
|
adantr |
|
11 |
10
|
3ad2ant1 |
|
12 |
|
simpr |
|
13 |
12
|
3ad2ant1 |
|
14 |
|
simpl |
|
15 |
14
|
3ad2ant1 |
|
16 |
15
|
adantr |
|
17 |
|
elmapi |
|
18 |
|
ffvelrn |
|
19 |
18
|
ex |
|
20 |
17 19
|
syl |
|
21 |
20
|
adantr |
|
22 |
21
|
3ad2ant2 |
|
23 |
22
|
imp |
|
24 |
|
elelpwi |
|
25 |
24
|
expcom |
|
26 |
25
|
adantl |
|
27 |
26
|
3ad2ant1 |
|
28 |
27
|
imp |
|
29 |
|
eqid |
|
30 |
7 4 29 5
|
lmodvscl |
|
31 |
16 23 28 30
|
syl3anc |
|
32 |
|
elmapi |
|
33 |
|
ffvelrn |
|
34 |
33
|
ex |
|
35 |
32 34
|
syl |
|
36 |
35
|
adantl |
|
37 |
36
|
3ad2ant2 |
|
38 |
37
|
imp |
|
39 |
7 4 29 5
|
lmodvscl |
|
40 |
16 38 28 39
|
syl3anc |
|
41 |
|
eqidd |
|
42 |
|
eqidd |
|
43 |
|
id |
|
44 |
|
simpl |
|
45 |
|
simpl |
|
46 |
4 5
|
scmfsupp |
|
47 |
43 44 45 46
|
syl3an |
|
48 |
|
simpr |
|
49 |
|
simpr |
|
50 |
4 5
|
scmfsupp |
|
51 |
43 48 49 50
|
syl3an |
|
52 |
7 8 1 11 13 31 40 41 42 47 51
|
gsummptfsadd |
|
53 |
12
|
adantr |
|
54 |
|
elmapfn |
|
55 |
54
|
ad2antrl |
|
56 |
|
elmapfn |
|
57 |
56
|
ad2antll |
|
58 |
53 55 57
|
offvalfv |
|
59 |
58
|
3adant3 |
|
60 |
4
|
lmodfgrp |
|
61 |
|
grpmnd |
|
62 |
60 61
|
syl |
|
63 |
62
|
ad3antrrr |
|
64 |
|
ffvelrn |
|
65 |
64
|
ex |
|
66 |
17 65
|
syl |
|
67 |
66
|
ad2antrl |
|
68 |
67
|
imp |
|
69 |
4
|
fveq2i |
|
70 |
5 69
|
eqtri |
|
71 |
68 70
|
eleqtrdi |
|
72 |
|
ffvelrn |
|
73 |
72 70
|
eleqtrdi |
|
74 |
73
|
ex |
|
75 |
32 74
|
syl |
|
76 |
75
|
ad2antll |
|
77 |
76
|
imp |
|
78 |
4
|
eqcomi |
|
79 |
78
|
fveq2i |
|
80 |
79 6
|
mndcl |
|
81 |
63 71 77 80
|
syl3anc |
|
82 |
81
|
fmpttd |
|
83 |
|
fvex |
|
84 |
|
elmapg |
|
85 |
83 53 84
|
sylancr |
|
86 |
82 85
|
mpbird |
|
87 |
86
|
3adant3 |
|
88 |
59 87
|
eqeltrd |
|
89 |
|
lincval |
|
90 |
15 88 13 89
|
syl3anc |
|
91 |
54 56
|
anim12i |
|
92 |
91
|
adantl |
|
93 |
92
|
adantr |
|
94 |
53
|
anim1i |
|
95 |
|
fnfvof |
|
96 |
93 94 95
|
syl2anc |
|
97 |
6
|
a1i |
|
98 |
97
|
oveqd |
|
99 |
96 98
|
eqtrd |
|
100 |
99
|
oveq1d |
|
101 |
14
|
adantr |
|
102 |
101
|
adantr |
|
103 |
20
|
ad2antrl |
|
104 |
103
|
imp |
|
105 |
35
|
ad2antll |
|
106 |
105
|
imp |
|
107 |
26
|
adantr |
|
108 |
107
|
imp |
|
109 |
|
eqid |
|
110 |
4
|
fveq2i |
|
111 |
7 1 109 29 70 110
|
lmodvsdir |
|
112 |
102 104 106 108 111
|
syl13anc |
|
113 |
100 112
|
eqtrd |
|
114 |
113
|
mpteq2dva |
|
115 |
114
|
oveq2d |
|
116 |
115
|
3adant3 |
|
117 |
90 116
|
eqtrd |
|
118 |
2 3
|
oveq12i |
|
119 |
70
|
oveq1i |
|
120 |
119
|
eleq2i |
|
121 |
120
|
biimpi |
|
122 |
121
|
ad2antrl |
|
123 |
|
lincval |
|
124 |
101 122 53 123
|
syl3anc |
|
125 |
119
|
eleq2i |
|
126 |
125
|
biimpi |
|
127 |
126
|
ad2antll |
|
128 |
|
lincval |
|
129 |
101 127 53 128
|
syl3anc |
|
130 |
124 129
|
oveq12d |
|
131 |
130
|
3adant3 |
|
132 |
118 131
|
syl5eq |
|
133 |
52 117 132
|
3eqtr4rd |
|