Step |
Hyp |
Ref |
Expression |
1 |
|
opsqrlem2.1 |
|
2 |
|
opsqrlem2.2 |
|
3 |
|
opsqrlem2.3 |
|
4 |
|
opsqrlem6.4 |
|
5 |
|
fveq2 |
|
6 |
5
|
breq1d |
|
7 |
|
fveq2 |
|
8 |
7
|
breq1d |
|
9 |
|
fveq2 |
|
10 |
9
|
breq1d |
|
11 |
1 2 3
|
opsqrlem2 |
|
12 |
|
idleop |
|
13 |
11 12
|
eqbrtri |
|
14 |
|
idhmop |
|
15 |
1 2 3
|
opsqrlem4 |
|
16 |
15
|
ffvelrni |
|
17 |
|
hmopd |
|
18 |
14 16 17
|
sylancr |
|
19 |
|
eqid |
|
20 |
|
hmopco |
|
21 |
19 20
|
mp3an3 |
|
22 |
18 18 21
|
syl2anc |
|
23 |
|
leopsq |
|
24 |
18 23
|
syl |
|
25 |
|
leop3 |
|
26 |
1 14 25
|
mp2an |
|
27 |
4 26
|
mpbi |
|
28 |
|
hmopd |
|
29 |
14 1 28
|
mp2an |
|
30 |
|
leopadd |
|
31 |
29 30
|
mpanl2 |
|
32 |
27 31
|
mpanr2 |
|
33 |
22 24 32
|
syl2anc |
|
34 |
|
2cn |
|
35 |
|
hmopf |
|
36 |
16 35
|
syl |
|
37 |
|
homulcl |
|
38 |
34 36 37
|
sylancr |
|
39 |
|
hmopf |
|
40 |
1 39
|
ax-mp |
|
41 |
|
fco |
|
42 |
36 36 41
|
syl2anc |
|
43 |
|
hosubcl |
|
44 |
40 42 43
|
sylancr |
|
45 |
|
hmopf |
|
46 |
14 45
|
ax-mp |
|
47 |
|
homulcl |
|
48 |
34 46 47
|
mp2an |
|
49 |
|
hosubsub4 |
|
50 |
48 49
|
mp3an1 |
|
51 |
38 44 50
|
syl2anc |
|
52 |
|
hosubcl |
|
53 |
42 38 52
|
syl2anc |
|
54 |
|
hoadd32 |
|
55 |
46 46 54
|
mp3an13 |
|
56 |
53 55
|
syl |
|
57 |
|
ho2times |
|
58 |
46 57
|
ax-mp |
|
59 |
58
|
oveq1i |
|
60 |
56 59
|
eqtr4di |
|
61 |
|
hoaddsubass |
|
62 |
48 61
|
mp3an1 |
|
63 |
42 38 62
|
syl2anc |
|
64 |
60 63
|
eqtr4d |
|
65 |
64
|
oveq1d |
|
66 |
|
hoaddcl |
|
67 |
46 53 66
|
sylancr |
|
68 |
|
hoaddsubass |
|
69 |
46 40 68
|
mp3an23 |
|
70 |
67 69
|
syl |
|
71 |
|
hoaddcl |
|
72 |
48 42 71
|
sylancr |
|
73 |
|
hosubsub4 |
|
74 |
40 73
|
mp3an3 |
|
75 |
72 38 74
|
syl2anc |
|
76 |
65 70 75
|
3eqtr3d |
|
77 |
|
hosubadd4 |
|
78 |
40 77
|
mpanr1 |
|
79 |
48 78
|
mpanl1 |
|
80 |
38 42 79
|
syl2anc |
|
81 |
76 80
|
eqtr4d |
|
82 |
|
halfcn |
|
83 |
|
homulcl |
|
84 |
82 44 83
|
sylancr |
|
85 |
|
hoadddi |
|
86 |
34 85
|
mp3an1 |
|
87 |
36 84 86
|
syl2anc |
|
88 |
|
2ne0 |
|
89 |
34 88
|
recidi |
|
90 |
89
|
oveq1i |
|
91 |
|
homulass |
|
92 |
34 82 91
|
mp3an12 |
|
93 |
44 92
|
syl |
|
94 |
|
homulid2 |
|
95 |
44 94
|
syl |
|
96 |
90 93 95
|
3eqtr3a |
|
97 |
96
|
oveq2d |
|
98 |
87 97
|
eqtrd |
|
99 |
98
|
oveq2d |
|
100 |
51 81 99
|
3eqtr4d |
|
101 |
|
hoaddcl |
|
102 |
36 84 101
|
syl2anc |
|
103 |
|
hosubdi |
|
104 |
34 46 103
|
mp3an12 |
|
105 |
102 104
|
syl |
|
106 |
100 105
|
eqtr4d |
|
107 |
|
hosubcl |
|
108 |
46 36 107
|
sylancr |
|
109 |
|
hocsubdir |
|
110 |
46 109
|
mp3an1 |
|
111 |
36 108 110
|
syl2anc |
|
112 |
|
hmoplin |
|
113 |
14 112
|
ax-mp |
|
114 |
|
hoddi |
|
115 |
113 46 114
|
mp3an12 |
|
116 |
36 115
|
syl |
|
117 |
46
|
hoid1i |
|
118 |
117
|
a1i |
|
119 |
|
hoico2 |
|
120 |
36 119
|
syl |
|
121 |
118 120
|
oveq12d |
|
122 |
116 121
|
eqtrd |
|
123 |
|
hmoplin |
|
124 |
16 123
|
syl |
|
125 |
|
hoddi |
|
126 |
46 125
|
mp3an2 |
|
127 |
124 36 126
|
syl2anc |
|
128 |
|
hoico1 |
|
129 |
36 128
|
syl |
|
130 |
129
|
oveq1d |
|
131 |
127 130
|
eqtrd |
|
132 |
122 131
|
oveq12d |
|
133 |
36 46
|
jctil |
|
134 |
|
hosubadd4 |
|
135 |
133 36 42 134
|
syl12anc |
|
136 |
132 135
|
eqtrd |
|
137 |
|
ho2times |
|
138 |
36 137
|
syl |
|
139 |
138
|
oveq2d |
|
140 |
|
hoaddsubass |
|
141 |
46 140
|
mp3an1 |
|
142 |
42 38 141
|
syl2anc |
|
143 |
136 139 142
|
3eqtr2d |
|
144 |
111 143
|
eqtrd |
|
145 |
144
|
oveq1d |
|
146 |
1 2 3
|
opsqrlem5 |
|
147 |
146
|
oveq2d |
|
148 |
147
|
oveq2d |
|
149 |
106 145 148
|
3eqtr4d |
|
150 |
33 149
|
breqtrd |
|
151 |
|
peano2nn |
|
152 |
15
|
ffvelrni |
|
153 |
151 152
|
syl |
|
154 |
|
hmopd |
|
155 |
14 153 154
|
sylancr |
|
156 |
|
2re |
|
157 |
|
2pos |
|
158 |
|
leopmul |
|
159 |
156 157 158
|
mp3an13 |
|
160 |
155 159
|
syl |
|
161 |
150 160
|
mpbird |
|
162 |
|
leop3 |
|
163 |
153 14 162
|
sylancl |
|
164 |
161 163
|
mpbird |
|
165 |
6 8 10 13 164
|
nn1suc |
|