Step | Hyp | Ref
| Expression |
1 | | oveq1 6208 |
. . . 4
             |
2 | 1 | oveq1d 6216 |
. . 3
                       |
3 | | oveq1 6208 |
. . 3
                       |
4 | 2, 3 | eqeq12d 2476 |
. 2
                     
                       |
5 | | oveq1 6208 |
. . . 4
                |
6 | 5 | oveq1d 6216 |
. . 3
                          |
7 | | oveq1 6208 |
. . 3
                          |
8 | 6, 7 | eqeq12d 2476 |
. 2
                                                 |
9 | | xmulcl 11348 |
. . . 4
          |
10 | 9 | 3adant3 1008 |
. . 3
          |
11 | | simp3 990 |
. . 3
     |
12 | | xmulcl 11348 |
. . 3
                    |
13 | 10, 11, 12 | syl2anc 661 |
. 2
               |
14 | | simp1 988 |
. . 3
     |
15 | | xmulcl 11348 |
. . . 4
          |
16 | 15 | 3adant1 1006 |
. . 3
          |
17 | | xmulcl 11348 |
. . 3
                    |
18 | 14, 16, 17 | syl2anc 661 |
. 2
               |
19 | | oveq2 6209 |
. . . . 5
             |
20 | 19 | oveq1d 6216 |
. . . 4
                       |
21 | | oveq1 6208 |
. . . . 5
             |
22 | 21 | oveq2d 6217 |
. . . 4
                       |
23 | 20, 22 | eqeq12d 2476 |
. . 3
                     
                       |
24 | | oveq2 6209 |
. . . . 5
                |
25 | 24 | oveq1d 6216 |
. . . 4
                          |
26 | | oveq1 6208 |
. . . . 5
                |
27 | 26 | oveq2d 6217 |
. . . 4
                          |
28 | 25, 27 | eqeq12d 2476 |
. . 3
                                                 |
29 | | simprl 755 |
. . . . 5
      
  |
30 | | simpl2 992 |
. . . . 5
      
  |
31 | | xmulcl 11348 |
. . . . 5
          |
32 | 29, 30, 31 | syl2anc 661 |
. . . 4
              |
33 | 11 | adantr 465 |
. . . 4
      
  |
34 | | xmulcl 11348 |
. . . 4
                    |
35 | 32, 33, 34 | syl2anc 661 |
. . 3
                   |
36 | 16 | adantr 465 |
. . . 4
              |
37 | | xmulcl 11348 |
. . . 4
                    |
38 | 29, 36, 37 | syl2anc 661 |
. . 3
                   |
39 | | oveq2 6209 |
. . . . 5
                       |
40 | | oveq2 6209 |
. . . . . 6
             |
41 | 40 | oveq2d 6217 |
. . . . 5
                       |
42 | 39, 41 | eqeq12d 2476 |
. . . 4
                     
                       |
43 | | oveq2 6209 |
. . . . 5
                          |
44 | | oveq2 6209 |
. . . . . 6
                |
45 | 44 | oveq2d 6217 |
. . . . 5
                          |
46 | 43, 45 | eqeq12d 2476 |
. . . 4
                                                 |
47 | 29 | adantr 465 |
. . . . . 6
   
 
    
  |
48 | | simprl 755 |
. . . . . 6
   
 
       |
49 | | xmulcl 11348 |
. . . . . 6
          |
50 | 47, 48, 49 | syl2anc 661 |
. . . . 5
   
 
            |
51 | 33 | adantr 465 |
. . . . 5
   
 
    
  |
52 | | xmulcl 11348 |
. . . . 5
                    |
53 | 50, 51, 52 | syl2anc 661 |
. . . 4
   
 
                 |
54 | | xmulcl 11348 |
. . . . . 6
          |
55 | 48, 51, 54 | syl2anc 661 |
. . . . 5
   
 
            |
56 | | xmulcl 11348 |
. . . . 5
                    |
57 | 47, 55, 56 | syl2anc 661 |
. . . 4
   
 
                 |
58 | | xmulasslem3 11361 |
. . . . . 6
    
 
                        |
59 | 58 | 3expa 1188 |
. . . . 5
   
 
    
                      |
60 | 59 | adantlll 717 |
. . . 4
    
 
     
                        |
61 | | xmul01 11342 |
. . . . . . . 8
                  |
62 | 50, 61 | syl 16 |
. . . . . . 7
   
 
                 |
63 | | xmul01 11342 |
. . . . . . . 8

       |
64 | 47, 63 | syl 16 |
. . . . . . 7
   
 
            |
65 | 62, 64 | eqtr4d 2498 |
. . . . . 6
   
 
                      |
66 | | xmul01 11342 |
. . . . . . . 8

       |
67 | 66 | ad2antrl 727 |
. . . . . . 7
   
 
            |
68 | 67 | oveq2d 6217 |
. . . . . 6
   
 
                      |
69 | 65, 68 | eqtr4d 2498 |
. . . . 5
   
 
                           |
70 | | oveq2 6209 |
. . . . . 6
                       |
71 | | oveq2 6209 |
. . . . . . 7
             |
72 | 71 | oveq2d 6217 |
. . . . . 6
                       |
73 | 70, 72 | eqeq12d 2476 |
. . . . 5
                     
                       |
74 | 69, 73 | syl5ibrcom 222 |
. . . 4
   
 
                             |
75 | | xmulneg2 11345 |
. . . . 5
                                 |
76 | 50, 51, 75 | syl2anc 661 |
. . . 4
   
 
                              |
77 | | xmulneg2 11345 |
. . . . . . 7
                  |
78 | 48, 51, 77 | syl2anc 661 |
. . . . . 6
   
 
                    |
79 | 78 | oveq2d 6217 |
. . . . 5
   
 
                             |
80 | | xmulneg2 11345 |
. . . . . 6
                                 |
81 | 47, 55, 80 | syl2anc 661 |
. . . . 5
   
 
                              |
82 | 79, 81 | eqtrd 2495 |
. . . 4
   
 
                              |
83 | 42, 46, 53, 57, 51, 60, 74, 76, 82 | xmulasslem 11360 |
. . 3
   
 
                           |
84 | | xmul02 11343 |
. . . . . . . 8

       |
85 | 84 | 3ad2ant3 1011 |
. . . . . . 7
          |
86 | 85 | adantr 465 |
. . . . . 6
              |
87 | 63 | ad2antrl 727 |
. . . . . 6
              |
88 | 86, 87 | eqtr4d 2498 |
. . . . 5
                   |
89 | 87 | oveq1d 6216 |
. . . . 5
                        |
90 | 86 | oveq2d 6217 |
. . . . 5
                        |
91 | 88, 89, 90 | 3eqtr4d 2505 |
. . . 4
                             |
92 | | oveq2 6209 |
. . . . . 6
             |
93 | 92 | oveq1d 6216 |
. . . . 5
                       |
94 | | oveq1 6208 |
. . . . . 6
             |
95 | 94 | oveq2d 6217 |
. . . . 5
                       |
96 | 93, 95 | eqeq12d 2476 |
. . . 4
                     
                       |
97 | 91, 96 | syl5ibrcom 222 |
. . 3
                               |
98 | | xmulneg2 11345 |
. . . . . 6
                  |
99 | 29, 30, 98 | syl2anc 661 |
. . . . 5
                      |
100 | 99 | oveq1d 6216 |
. . . 4
                               |
101 | | xmulneg1 11344 |
. . . . 5
                                 |
102 | 32, 33, 101 | syl2anc 661 |
. . . 4
                                |
103 | 100, 102 | eqtrd 2495 |
. . 3
                                |
104 | | xmulneg1 11344 |
. . . . . 6
                  |
105 | 30, 33, 104 | syl2anc 661 |
. . . . 5
                      |
106 | 105 | oveq2d 6217 |
. . . 4
                               |
107 | | xmulneg2 11345 |
. . . . 5
                                 |
108 | 29, 36, 107 | syl2anc 661 |
. . . 4
                                |
109 | 106, 108 | eqtrd 2495 |
. . 3
                                |
110 | 23, 28, 35, 38, 30, 83, 97, 103, 109 | xmulasslem 11360 |
. 2
                             |
111 | | xmul02 11343 |
. . . . . 6

       |
112 | 111 | 3ad2ant2 1010 |
. . . . 5
          |
113 | 112 | oveq1d 6216 |
. . . 4
                    |
114 | | xmul02 11343 |
. . . . 5
                  |
115 | 16, 114 | syl 16 |
. . . 4
               |
116 | 85, 113, 115 | 3eqtr4d 2505 |
. . 3
                         |
117 | | oveq1 6208 |
. . . . 5
             |
118 | 117 | oveq1d 6216 |
. . . 4
                       |
119 | | oveq1 6208 |
. . . 4
                       |
120 | 118, 119 | eqeq12d 2476 |
. . 3
                     
                       |
121 | 116, 120 | syl5ibrcom 222 |
. 2
                           |
122 | | xmulneg1 11344 |
. . . . 5
                  |
123 | 122 | 3adant3 1008 |
. . . 4
                  |
124 | 123 | oveq1d 6216 |
. . 3
                           |
125 | | xmulneg1 11344 |
. . . 4
                                 |
126 | 10, 11, 125 | syl2anc 661 |
. . 3
                            |
127 | 124, 126 | eqtrd 2495 |
. 2
                            |
128 | | xmulneg1 11344 |
. . 3
                                 |
129 | 14, 16, 128 | syl2anc 661 |
. 2
                            |
130 | 4, 8, 13, 18, 14, 110, 121, 127, 129 | xmulasslem 11360 |
1
                         |