Step |
Hyp |
Ref |
Expression |
1 |
|
itgmulc2nc.1 |
|
2 |
|
itgmulc2nc.2 |
|
3 |
|
itgmulc2nc.3 |
|
4 |
|
itgmulc2nc.m |
|
5 |
1
|
recld |
|
6 |
5
|
recnd |
|
7 |
6
|
adantr |
|
8 |
|
iblmbf |
|
9 |
3 8
|
syl |
|
10 |
9 2
|
mbfmptcl |
|
11 |
10
|
recld |
|
12 |
11
|
recnd |
|
13 |
7 12
|
mulcld |
|
14 |
10
|
iblcn |
|
15 |
3 14
|
mpbid |
|
16 |
15
|
simpld |
|
17 |
|
ovexd |
|
18 |
4 17
|
mbfdm2 |
|
19 |
|
fconstmpt |
|
20 |
19
|
a1i |
|
21 |
|
eqidd |
|
22 |
18 7 11 20 21
|
offval2 |
|
23 |
|
iblmbf |
|
24 |
16 23
|
syl |
|
25 |
12
|
fmpttd |
|
26 |
24 5 25
|
mbfmulc2re |
|
27 |
22 26
|
eqeltrrd |
|
28 |
6 11 16 27
|
iblmulc2nc |
|
29 |
13 28
|
itgcl |
|
30 |
|
ax-icn |
|
31 |
10
|
imcld |
|
32 |
31
|
recnd |
|
33 |
7 32
|
mulcld |
|
34 |
15
|
simprd |
|
35 |
|
eqidd |
|
36 |
18 7 31 20 35
|
offval2 |
|
37 |
|
iblmbf |
|
38 |
34 37
|
syl |
|
39 |
32
|
fmpttd |
|
40 |
38 5 39
|
mbfmulc2re |
|
41 |
36 40
|
eqeltrrd |
|
42 |
6 31 34 41
|
iblmulc2nc |
|
43 |
33 42
|
itgcl |
|
44 |
|
mulcl |
|
45 |
30 43 44
|
sylancr |
|
46 |
1
|
imcld |
|
47 |
46
|
recnd |
|
48 |
47
|
negcld |
|
49 |
48
|
adantr |
|
50 |
49 32
|
mulcld |
|
51 |
|
fconstmpt |
|
52 |
51
|
a1i |
|
53 |
18 49 31 52 35
|
offval2 |
|
54 |
46
|
renegcld |
|
55 |
38 54 39
|
mbfmulc2re |
|
56 |
53 55
|
eqeltrrd |
|
57 |
48 31 34 56
|
iblmulc2nc |
|
58 |
50 57
|
itgcl |
|
59 |
47
|
adantr |
|
60 |
59 12
|
mulcld |
|
61 |
|
fconstmpt |
|
62 |
61
|
a1i |
|
63 |
18 59 11 62 21
|
offval2 |
|
64 |
24 46 25
|
mbfmulc2re |
|
65 |
63 64
|
eqeltrrd |
|
66 |
47 11 16 65
|
iblmulc2nc |
|
67 |
60 66
|
itgcl |
|
68 |
|
mulcl |
|
69 |
30 67 68
|
sylancr |
|
70 |
29 45 58 69
|
add4d |
|
71 |
30
|
a1i |
|
72 |
71 47
|
mulcld |
|
73 |
2 3
|
itgcl |
|
74 |
6 72 73
|
adddird |
|
75 |
2 3
|
itgcnval |
|
76 |
75
|
oveq2d |
|
77 |
11 16
|
itgcl |
|
78 |
31 34
|
itgcl |
|
79 |
|
mulcl |
|
80 |
30 78 79
|
sylancr |
|
81 |
6 77 80
|
adddid |
|
82 |
6 11 16 27 5 11
|
itgmulc2nclem2 |
|
83 |
6 71 78
|
mul12d |
|
84 |
6 31 34 41 5 31
|
itgmulc2nclem2 |
|
85 |
84
|
oveq2d |
|
86 |
83 85
|
eqtrd |
|
87 |
82 86
|
oveq12d |
|
88 |
76 81 87
|
3eqtrd |
|
89 |
75
|
oveq2d |
|
90 |
72 77 80
|
adddid |
|
91 |
71 47 77
|
mulassd |
|
92 |
47 11 16 65 46 11
|
itgmulc2nclem2 |
|
93 |
92
|
oveq2d |
|
94 |
91 93
|
eqtrd |
|
95 |
71 47 71 78
|
mul4d |
|
96 |
|
ixi |
|
97 |
96
|
oveq1i |
|
98 |
47 78
|
mulcld |
|
99 |
98
|
mulm1d |
|
100 |
97 99
|
syl5eq |
|
101 |
47 78
|
mulneg1d |
|
102 |
48 31 34 56 54 31
|
itgmulc2nclem2 |
|
103 |
101 102
|
eqtr3d |
|
104 |
95 100 103
|
3eqtrd |
|
105 |
94 104
|
oveq12d |
|
106 |
69 58
|
addcomd |
|
107 |
105 106
|
eqtrd |
|
108 |
89 90 107
|
3eqtrd |
|
109 |
88 108
|
oveq12d |
|
110 |
74 109
|
eqtrd |
|
111 |
59 32
|
mulcld |
|
112 |
18 59 31 62 35
|
offval2 |
|
113 |
38 46 39
|
mbfmulc2re |
|
114 |
112 113
|
eqeltrrd |
|
115 |
47 31 34 114
|
iblmulc2nc |
|
116 |
1
|
adantr |
|
117 |
116 10
|
mulcld |
|
118 |
|
eqidd |
|
119 |
|
ref |
|
120 |
119
|
a1i |
|
121 |
120
|
feqmptd |
|
122 |
|
fveq2 |
|
123 |
117 118 121 122
|
fmptco |
|
124 |
116 10
|
remuld |
|
125 |
124
|
mpteq2dva |
|
126 |
123 125
|
eqtrd |
|
127 |
117
|
fmpttd |
|
128 |
|
ismbfcn |
|
129 |
127 128
|
syl |
|
130 |
4 129
|
mpbid |
|
131 |
130
|
simpld |
|
132 |
126 131
|
eqeltrrd |
|
133 |
13 28 111 115 132
|
itgsubnc |
|
134 |
124
|
itgeq2dv |
|
135 |
111 115
|
itgneg |
|
136 |
59 32
|
mulneg1d |
|
137 |
136
|
itgeq2dv |
|
138 |
135 137
|
eqtr4d |
|
139 |
138
|
oveq2d |
|
140 |
111 115
|
itgcl |
|
141 |
29 140
|
negsubd |
|
142 |
139 141
|
eqtr3d |
|
143 |
133 134 142
|
3eqtr4d |
|
144 |
116 10
|
immuld |
|
145 |
144
|
itgeq2dv |
|
146 |
|
imf |
|
147 |
146
|
a1i |
|
148 |
147
|
feqmptd |
|
149 |
|
fveq2 |
|
150 |
117 118 148 149
|
fmptco |
|
151 |
144
|
mpteq2dva |
|
152 |
150 151
|
eqtrd |
|
153 |
130
|
simprd |
|
154 |
152 153
|
eqeltrrd |
|
155 |
33 42 60 66 154
|
itgaddnc |
|
156 |
145 155
|
eqtrd |
|
157 |
156
|
oveq2d |
|
158 |
71 43 67
|
adddid |
|
159 |
157 158
|
eqtrd |
|
160 |
143 159
|
oveq12d |
|
161 |
70 110 160
|
3eqtr4d |
|
162 |
1
|
replimd |
|
163 |
162
|
oveq1d |
|
164 |
1 2 3 4
|
iblmulc2nc |
|
165 |
117 164
|
itgcnval |
|
166 |
161 163 165
|
3eqtr4d |
|