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, Function, V, s
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 ScalarMult, TensorProd
from proveit.logic import InSet

# build up the expression from sub-expressions
expr = Conditional(InSet(TensorProd(a_1_to_i, ScalarMult(Function(s, [b_1_to_j]), f__b_1_to_j), c_1_to_k), V), Q__b_1_to_j)

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} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left(s\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right) \in V \textrm{ if } Q\left(b_{1}, b_{2}, \ldots, b_{j}\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: 3 operands: 4
2	Operation	operator: 5 operands: 26
3	Literal
4	ExprTuple	6, 7
5	Variable
6	Operation	operator: 8 operands: 9
7	Variable
8	Literal
9	ExprTuple	10, 11, 12
10	ExprRange	lambda_map: 13 start_index: 30 end_index: 14
11	Operation	operator: 15 operands: 16
12	ExprRange	lambda_map: 17 start_index: 30 end_index: 18
13	Lambda	parameter: 35 body: 19
14	Variable
15	Literal
16	ExprTuple	20, 21
17	Lambda	parameter: 35 body: 22
18	Variable
19	IndexedVar	variable: 23 index: 35
20	Operation	operator: 24 operands: 26
21	Operation	operator: 25 operands: 26
22	IndexedVar	variable: 27 index: 35
23	Variable
24	Variable
25	Variable
26	ExprTuple	28
27	Variable
28	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
29	Lambda	parameter: 35 body: 32
30	Literal
31	Variable
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable