Step |
Hyp |
Ref |
Expression |
1 |
|
gsumesum.0 |
|
2 |
|
gsumesum.1 |
|
3 |
|
gsumesum.2 |
|
4 |
|
nfcv |
|
5 |
|
eqidd |
|
6 |
1 4 2 3 5
|
esumval |
|
7 |
|
xrltso |
|
8 |
7
|
a1i |
|
9 |
|
iccssxr |
|
10 |
|
xrge0base |
|
11 |
|
xrge0cmn |
|
12 |
11
|
a1i |
|
13 |
3
|
ex |
|
14 |
1 13
|
ralrimi |
|
15 |
10 12 2 14
|
gsummptcl |
|
16 |
9 15
|
sseldi |
|
17 |
|
pwidg |
|
18 |
2 17
|
syl |
|
19 |
18 2
|
elind |
|
20 |
|
eqidd |
|
21 |
|
mpteq1 |
|
22 |
21
|
oveq2d |
|
23 |
22
|
rspceeqv |
|
24 |
19 20 23
|
syl2anc |
|
25 |
|
eqid |
|
26 |
|
ovex |
|
27 |
25 26
|
elrnmpti |
|
28 |
24 27
|
sylibr |
|
29 |
|
simpr |
|
30 |
|
mpteq1 |
|
31 |
30
|
oveq2d |
|
32 |
31
|
cbvmptv |
|
33 |
|
ovex |
|
34 |
32 33
|
elrnmpti |
|
35 |
29 34
|
sylib |
|
36 |
11
|
a1i |
|
37 |
|
inss2 |
|
38 |
|
simpr |
|
39 |
37 38
|
sseldi |
|
40 |
|
nfv |
|
41 |
1 40
|
nfan |
|
42 |
|
simpll |
|
43 |
|
inss1 |
|
44 |
43
|
sseli |
|
45 |
44
|
elpwid |
|
46 |
45
|
ad2antlr |
|
47 |
|
simpr |
|
48 |
46 47
|
sseldd |
|
49 |
42 48 3
|
syl2anc |
|
50 |
49
|
ex |
|
51 |
41 50
|
ralrimi |
|
52 |
10 36 39 51
|
gsummptcl |
|
53 |
9 52
|
sseldi |
|
54 |
|
diffi |
|
55 |
2 54
|
syl |
|
56 |
55
|
adantr |
|
57 |
|
simpll |
|
58 |
|
simpr |
|
59 |
58
|
eldifad |
|
60 |
57 59 3
|
syl2anc |
|
61 |
60
|
ex |
|
62 |
41 61
|
ralrimi |
|
63 |
10 36 56 62
|
gsummptcl |
|
64 |
9 63
|
sseldi |
|
65 |
|
elxrge0 |
|
66 |
65
|
simprbi |
|
67 |
63 66
|
syl |
|
68 |
|
xraddge02 |
|
69 |
68
|
imp |
|
70 |
53 64 67 69
|
syl21anc |
|
71 |
70
|
adantlr |
|
72 |
|
simpll |
|
73 |
45
|
adantl |
|
74 |
|
xrge00 |
|
75 |
|
xrge0plusg |
|
76 |
11
|
a1i |
|
77 |
2
|
adantr |
|
78 |
|
eqid |
|
79 |
1 3 78
|
fmptdf |
|
80 |
79
|
adantr |
|
81 |
78
|
fnmpt |
|
82 |
14 81
|
syl |
|
83 |
|
c0ex |
|
84 |
83
|
a1i |
|
85 |
82 2 84
|
fndmfifsupp |
|
86 |
85
|
adantr |
|
87 |
|
disjdif |
|
88 |
87
|
a1i |
|
89 |
|
undif |
|
90 |
89
|
biimpi |
|
91 |
90
|
eqcomd |
|
92 |
91
|
adantl |
|
93 |
10 74 75 76 77 80 86 88 92
|
gsumsplit |
|
94 |
|
resmpt |
|
95 |
94
|
oveq2d |
|
96 |
95
|
adantl |
|
97 |
|
difss |
|
98 |
|
resmpt |
|
99 |
97 98
|
ax-mp |
|
100 |
99
|
oveq2i |
|
101 |
100
|
a1i |
|
102 |
96 101
|
oveq12d |
|
103 |
93 102
|
eqtrd |
|
104 |
72 73 103
|
syl2anc |
|
105 |
71 104
|
breqtrrd |
|
106 |
105
|
ralrimiva |
|
107 |
|
r19.29r |
|
108 |
|
breq1 |
|
109 |
108
|
biimpar |
|
110 |
109
|
rexlimivw |
|
111 |
107 110
|
syl |
|
112 |
35 106 111
|
syl2anc |
|
113 |
16
|
adantr |
|
114 |
11
|
a1i |
|
115 |
|
simpr |
|
116 |
37 115
|
sseldi |
|
117 |
|
nfv |
|
118 |
1 117
|
nfan |
|
119 |
|
simpll |
|
120 |
43
|
sseli |
|
121 |
120
|
ad2antlr |
|
122 |
121
|
elpwid |
|
123 |
|
simpr |
|
124 |
122 123
|
sseldd |
|
125 |
119 124 3
|
syl2anc |
|
126 |
125
|
ex |
|
127 |
118 126
|
ralrimi |
|
128 |
10 114 116 127
|
gsummptcl |
|
129 |
9 128
|
sseldi |
|
130 |
129
|
ralrimiva |
|
131 |
25
|
rnmptss |
|
132 |
130 131
|
syl |
|
133 |
132
|
sselda |
|
134 |
|
xrltnle |
|
135 |
134
|
con2bid |
|
136 |
113 133 135
|
syl2anc |
|
137 |
112 136
|
mpbid |
|
138 |
8 16 28 137
|
supmax |
|
139 |
6 138
|
eqtr2d |
|