Expression of type Conditional

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, K, 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 = 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(TensorProd(a_1_to_i, vec_summation_b1toj_fQ, c_1_to_k), VecSum(index_or_indices = sub_expr1, summand = sub_expr2, condition = Q__b_1_to_j)).with_wrapping_at(1)).with_wrapping_at(2)).with_wrapping(), 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\{\begin{array}{l}\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(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) \\  = \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] \end{array} \end{array}\right) \end{array} \end{array}\right)\end{array} \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 17 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	35, 7
6	Lambda	parameters: 8 body: 9
7	Operation	operator: 10 operand: 14
8	ExprTuple	42, 44
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	15, 16
14	Variable
15	Operation	operator: 17 operand: 21
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21
19	Literal
20	ExprTuple	22, 23
21	Lambda	parameters: 49 body: 24
22	Operation	operator: 39 operands: 25
23	Operation	operator: 32 operand: 29
24	Conditional	value: 27 condition: 41
25	ExprTuple	42, 28, 44
26	ExprTuple	29
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operand: 36
29	Lambda	parameters: 49 body: 34
30	Literal
31	ExprTuple	37, 35
32	Literal
33	ExprTuple	36
34	Conditional	value: 37 condition: 41
35	Variable
36	Lambda	parameters: 49 body: 38
37	Operation	operator: 39 operands: 40
38	Conditional	value: 43 condition: 41
39	Literal
40	ExprTuple	42, 43, 44
41	Operation	operator: 45 operands: 49
42	ExprRange	lambda_map: 46 start_index: 57 end_index: 47
43	Operation	operator: 48 operands: 49
44	ExprRange	lambda_map: 50 start_index: 57 end_index: 51
45	Variable
46	Lambda	parameter: 63 body: 52
47	Variable
48	Variable
49	ExprTuple	53
50	Lambda	parameter: 63 body: 54
51	Variable
52	IndexedVar	variable: 55 index: 63
53	ExprRange	lambda_map: 56 start_index: 57 end_index: 58
54	IndexedVar	variable: 59 index: 63
55	Variable
56	Lambda	parameter: 63 body: 60
57	Literal
58	Variable
59	Variable
60	IndexedVar	variable: 61 index: 63
61	Variable
62	ExprTuple	63
63	Variable