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, ExprTuple, K, Lambda, V
from proveit.core_expr_types import Q__b_1_to_j, a_1_to_i, b_1_to_j, c_1_to_k, f__b_1_to_j
from proveit.linear_algebra import TensorProd, VecSpaces, VecSum
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Forall, Implies, InClass, InSet

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
sub_expr2 = TensorProd(a_1_to_i, f__b_1_to_j, c_1_to_k)
expr = ExprTuple(Lambda(V, Conditional(Forall(instance_param_or_params = [a_1_to_i, c_1_to_k], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr2, V), condition = Q__b_1_to_j), Equals(VecSum(index_or_indices = sub_expr1, summand = sub_expr2, condition = Q__b_1_to_j), TensorProd(a_1_to_i, vec_summation_b1toj_fQ, c_1_to_k)).with_wrapping_at(1)).with_wrapping_at(2)), InClass(V, VecSpaces(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(V \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{k}}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} f\left(b_{1}, b_{2}, \ldots, b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \in V\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} f\left(b_{1}, b_{2}, \ldots, b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right)\right] \\  = \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right]{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \end{array} \end{array}\right) \end{array} \end{array}\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(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	parameter: 38 body: 3
2	ExprTuple	38
3	Conditional	value: 4 condition: 5
4	Operation	operator: 20 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	38, 10
9	Lambda	parameters: 11 body: 12
10	Operation	operator: 13 operand: 17
11	ExprTuple	44, 45
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17
15	Literal
16	ExprTuple	18, 19
17	Variable
18	Operation	operator: 20 operand: 24
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24
22	Literal
23	ExprTuple	25, 26
24	Lambda	parameters: 54 body: 27
25	Operation	operator: 36 operand: 31
26	Operation	operator: 41 operands: 29
27	Conditional	value: 30 condition: 47
28	ExprTuple	31
29	ExprTuple	44, 32, 45
30	Operation	operator: 33 operands: 34
31	Lambda	parameters: 54 body: 35
32	Operation	operator: 36 operand: 40
33	Literal
34	ExprTuple	39, 38
35	Conditional	value: 39 condition: 47
36	Literal
37	ExprTuple	40
38	Variable
39	Operation	operator: 41 operands: 42
40	Lambda	parameters: 54 body: 43
41	Literal
42	ExprTuple	44, 46, 45
43	Conditional	value: 46 condition: 47
44	ExprRange	lambda_map: 48 start_index: 61 end_index: 49
45	ExprRange	lambda_map: 50 start_index: 61 end_index: 51
46	Operation	operator: 52 operands: 54
47	Operation	operator: 53 operands: 54
48	Lambda	parameter: 66 body: 55
49	Variable
50	Lambda	parameter: 66 body: 56
51	Variable
52	Variable
53	Variable
54	ExprTuple	57
55	IndexedVar	variable: 58 index: 66
56	IndexedVar	variable: 59 index: 66
57	ExprRange	lambda_map: 60 start_index: 61 end_index: 62
58	Variable
59	Variable
60	Lambda	parameter: 66 body: 63
61	Literal
62	Variable
63	IndexedVar	variable: 64 index: 66
64	Variable
65	ExprTuple	66
66	Variable