Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, U, V, Variable, W, a, b, c, d, e, f, i, k
from proveit.core_expr_types import a_1_to_i, c_1_to_k, d_1_to_i, f_1_to_k
from proveit.linear_algebra import TensorProd, VecZero
from proveit.logic import And, Equals, Forall, Implies, InSet, NotEquals
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(U, sub_expr1)
sub_expr3 = IndexedVar(W, sub_expr1)
expr = ExprTuple(Lambda([a_1_to_i, c_1_to_k, d_1_to_i, f_1_to_k], Conditional(Forall(instance_param_or_params = [b, e], instance_expr = Implies(Equals(TensorProd(a_1_to_i, b, c_1_to_k), TensorProd(d_1_to_i, e, f_1_to_k)).with_wrapping_at(2), Equals(TensorProd(a_1_to_i, c_1_to_k), TensorProd(d_1_to_i, f_1_to_k)).with_wrapping_at(2)).with_wrapping_at(2), domain = V, conditions = [Equals(b, e), NotEquals(b, VecZero(V))]), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), sub_expr2), one, i), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), sub_expr3), one, k), ExprRange(sub_expr1, InSet(IndexedVar(d, sub_expr1), sub_expr2), one, i), ExprRange(sub_expr1, InSet(IndexedVar(f, sub_expr1), sub_expr3), one, k)))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{k}, d_{1}, d_{2}, \ldots, d_{i}, f_{1}, f_{2}, \ldots, f_{k}\right) \mapsto \left\{\forall_{b, e \in V~|~b = e, b \neq \vec{0}\left(V\right)}~\left(\begin{array}{c} \begin{array}{l} \left(\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} b{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) =  \\ \left(d_{1} {\otimes}  d_{2} {\otimes}  \ldots {\otimes}  d_{i} {\otimes} e{\otimes} f_{1} {\otimes}  f_{2} {\otimes}  \ldots {\otimes}  f_{k}\right) \end{array} \end{array}\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i}{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) =  \\ \left(d_{1} {\otimes}  d_{2} {\otimes}  \ldots {\otimes}  d_{i}{\otimes} f_{1} {\otimes}  f_{2} {\otimes}  \ldots {\otimes}  f_{k}\right) \end{array} \end{array}\right) \end{array} \end{array}\right) \textrm{ if } \left(a_{1} \in U_{1}\right) ,  \left(a_{2} \in U_{2}\right) ,  \ldots ,  \left(a_{i} \in U_{i}\right), \left(c_{1} \in W_{1}\right) ,  \left(c_{2} \in W_{2}\right) ,  \ldots ,  \left(c_{k} \in W_{k}\right), \left(d_{1} \in U_{1}\right) ,  \left(d_{2} \in U_{2}\right) ,  \ldots ,  \left(d_{i} \in U_{i}\right), \left(f_{1} \in W_{1}\right) ,  \left(f_{2} \in W_{2}\right) ,  \ldots ,  \left(f_{k} \in W_{k}\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	66, 67, 68, 69
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 27 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12, 13
9	Lambda	parameters: 47 body: 14
10	ExprRange	lambda_map: 15 start_index: 76 end_index: 74
11	ExprRange	lambda_map: 16 start_index: 76 end_index: 77
12	ExprRange	lambda_map: 17 start_index: 76 end_index: 74
13	ExprRange	lambda_map: 18 start_index: 76 end_index: 77
14	Conditional	value: 19 condition: 20
15	Lambda	parameter: 87 body: 21
16	Lambda	parameter: 87 body: 22
17	Lambda	parameter: 87 body: 23
18	Lambda	parameter: 87 body: 24
19	Operation	operator: 25 operands: 26
20	Operation	operator: 27 operands: 28
21	Operation	operator: 44 operands: 29
22	Operation	operator: 44 operands: 30
23	Operation	operator: 44 operands: 31
24	Operation	operator: 44 operands: 32
25	Literal
26	ExprTuple	33, 34
27	Literal
28	ExprTuple	35, 36, 37, 38
29	ExprTuple	78, 39
30	ExprTuple	79, 40
31	ExprTuple	80, 39
32	ExprTuple	81, 40
33	Operation	operator: 46 operands: 41
34	Operation	operator: 46 operands: 42
35	Operation	operator: 44 operands: 43
36	Operation	operator: 44 operands: 45
37	Operation	operator: 46 operands: 47
38	Operation	operator: 48 operands: 49
39	IndexedVar	variable: 50 index: 87
40	IndexedVar	variable: 51 index: 87
41	ExprTuple	52, 53
42	ExprTuple	54, 55
43	ExprTuple	64, 70
44	Literal
45	ExprTuple	65, 70
46	Literal
47	ExprTuple	64, 65
48	Literal
49	ExprTuple	64, 56
50	Variable
51	Variable
52	Operation	operator: 60 operands: 57
53	Operation	operator: 60 operands: 58
54	Operation	operator: 60 operands: 59
55	Operation	operator: 60 operands: 61
56	Operation	operator: 62 operand: 70
57	ExprTuple	66, 64, 67
58	ExprTuple	68, 65, 69
59	ExprTuple	66, 67
60	Literal
61	ExprTuple	68, 69
62	Literal
63	ExprTuple	70
64	Variable
65	Variable
66	ExprRange	lambda_map: 71 start_index: 76 end_index: 74
67	ExprRange	lambda_map: 72 start_index: 76 end_index: 77
68	ExprRange	lambda_map: 73 start_index: 76 end_index: 74
69	ExprRange	lambda_map: 75 start_index: 76 end_index: 77
70	Variable
71	Lambda	parameter: 87 body: 78
72	Lambda	parameter: 87 body: 79
73	Lambda	parameter: 87 body: 80
74	Variable
75	Lambda	parameter: 87 body: 81
76	Literal
77	Variable
78	IndexedVar	variable: 82 index: 87
79	IndexedVar	variable: 83 index: 87
80	IndexedVar	variable: 84 index: 87
81	IndexedVar	variable: 85 index: 87
82	Variable
83	Variable
84	Variable
85	Variable
86	ExprTuple	87
87	Variable