-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathlB_non_unital.v
117 lines (58 loc) · 3.68 KB
/
lB_non_unital.v
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
(** ** Non unital lBsystems
By Vladimir Voevodsky, started on Jan. 16, 2015 *)
Unset Automatic Introduction.
Require Export lBsystems.TS_ST.
Require Export lBsystems.STid .
Require Export lBsystems.lB0.
(** Conditions TT and TTt *)
Definition TT_type { BB : lB0system_non_unital } :=
T_Tt.TT_type ( @T_ax0 BB ) ( @T_ax1a BB ) ( @T_ax1b BB ) .
Definition TTt_type { BB : lB0system_non_unital } :=
T_Tt.TTt_type ( @T_ax0 BB ) ( @T_ax1a BB ) ( @T_ax1b BB ) ( @Tt_ax1 BB ) .
Definition TT_TTt_layer ( BB : lB0system_non_unital ) := dirprod ( @TT_type BB ) ( @TTt_type BB ) .
(** Conditions SSt and StSt *)
Definition SSt_type { BB : lB0system_non_unital } :=
S_St.SSt_type ( @S_ax0 BB ) ( @S_ax1a BB ) ( @S_ax1b BB ) ( @St_ax1 BB ) .
Definition StSt_type { BB : lB0system_non_unital } :=
S_St.StSt_type ( @S_ax0 BB ) ( @S_ax1a BB ) ( @S_ax1b BB ) ( @St_ax1 BB ) .
Definition SSt_StSt_layer ( BB : lB0system_non_unital ) := dirprod ( @SSt_type BB ) ( @StSt_type BB ) .
(** Conditions TS and TtS *)
Definition TS_type { BB : lB0system_non_unital } :=
TS_ST.TS_type ( @T_ax1b BB ) ( @S_ax0 BB ) ( @S_ax1a BB ) ( @S_ax1b BB ) .
Definition TtS_type { BB : lB0system_non_unital } :=
TS_ST.TtS_type ( @T_ax1b BB ) ( @Tt_ax1 BB )
( @S_ax0 BB ) ( @S_ax1a BB ) ( @S_ax1b BB ) ( @St_ax1 BB ) .
Definition TS_TtS_layer ( BB : lB0system_non_unital ) := dirprod ( @TS_type BB ) ( @TtS_type BB ) .
(** Conditions STt and StTt *)
Definition STt_type { BB : lB0system_non_unital } :=
TS_ST.STt_type ( @T_ax0 BB ) ( @T_ax1a BB ) ( @Tt_ax1 BB ) ( @S_ax1b BB ) .
Definition StTt_type { BB : lB0system_non_unital } :=
TS_ST.StTt_type ( @T_ax0 BB ) ( @T_ax1a BB ) ( @Tt_ax1 BB ) ( @S_ax1b BB ) ( @St_ax1 BB ) .
Definition ST_StTt_layer ( BB : lB0system_non_unital ) := dirprod ( @STt_type BB ) ( @StTt_type BB ) .
(** Conditions STid and StTtid *)
Definition STid_type { BB : lB0system_non_unital } :=
STid.STid_type ( @T_ax1b BB ) ( @S_op BB ) .
Definition StTtid_type { BB : lB0system_non_unital } :=
STid.StTtid_type ( @T_ax1b BB ) ( @Tt_ax1 BB ) ( @St_op BB ) .
Definition STid_layer ( BB : lB0system_non_unital ) := dirprod ( @STid_type BB ) ( @StTtid_type BB ) .
(** Complete non-unital lBsystem *)
Definition lB_nu :=
total2 ( fun BB : lB0system_non_unital =>
dirprod
( dirprod
( dirprod ( TT_TTt_layer BB ) ( SSt_StSt_layer BB ) )
( dirprod ( TS_TtS_layer BB ) ( ST_StTt_layer BB ) ) )
( STid_layer BB ) ) .
Definition lB_nu_pr1 : lB_nu -> lB0system_non_unital := pr1 .
Coercion lB_nu_pr1 : lB_nu >-> lB0system_non_unital .
Definition TT { BB : lB_nu } : @TT_type BB := pr1 ( pr1 ( pr1 ( pr1 ( pr2 BB ) ) ) ) .
Definition TTt { BB : lB_nu } : @TTt_type BB := pr2 ( pr1 ( pr1 ( pr1 ( pr2 BB ) ) ) ) .
Definition SSt { BB : lB_nu } : @SSt_type BB := pr1 ( pr2 ( pr1 ( pr1 ( pr2 BB ) ) ) ) .
Definition StSt { BB : lB_nu } : @StSt_type BB := pr2 ( pr2 ( pr1 ( pr1 ( pr2 BB ) ) ) ) .
Definition TS { BB : lB_nu } : @TS_type BB := pr1 ( pr1 ( pr2 ( pr1 ( pr2 BB ) ) ) ) .
Definition TtS { BB : lB_nu } : @TtS_type BB := pr2 ( pr1 ( pr2 ( pr1 ( pr2 BB ) ) ) ) .
Definition STt { BB : lB_nu } : @STt_type BB := pr1 ( pr2 ( pr2 ( pr1 ( pr2 BB ) ) ) ) .
Definition StTt { BB : lB_nu } : @StTt_type BB := pr2 ( pr2 ( pr2 ( pr1 ( pr2 BB ) ) ) ) .
Definition STid_ax { BB : lB_nu } : @STid_type BB := pr1 ( pr2 ( pr2 BB ) ) .
Definition StTtid { BB : lB_nu } : @StTtid_type BB := pr2 ( pr2 ( pr2 BB ) ) .
(* End of the file lB_non_unital.v *)