Expression of type Conditional

from the theory of proveit.linear_algebra.scalar_multiplication

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, v
from proveit.core_expr_types import Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Implies, InSet
from proveit.numbers import Sum

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = Conditional(Implies(InSet(vec_summation_b1toj_fQ, K), Equals(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(f__b_1_to_j, v), condition = Q__b_1_to_j), ScalarMult(Sum(index_or_indices = sub_expr1, summand = f__b_1_to_j, condition = Q__b_1_to_j), v)).with_wrapping_at(1)).with_wrapping_at(2), InSet(v, V))

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}{c} \begin{array}{l} \left(\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] \in K\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(f\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot v\right)\right] \\  = \left(\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] \cdot v\right) \end{array} \end{array}\right) \end{array} \end{array} \textrm{ if } v \in V\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: 9 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	30, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 11 operands: 12
8	Variable
9	Literal
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15, 16
13	Operation	operator: 17 operand: 26
14	Variable
15	Operation	operator: 17 operand: 20
16	Operation	operator: 27 operands: 19
17	Literal
18	ExprTuple	20
19	ExprTuple	21, 30
20	Lambda	parameters: 35 body: 22
21	Operation	operator: 23 operand: 26
22	Conditional	value: 25 condition: 32
23	Literal
24	ExprTuple	26
25	Operation	operator: 27 operands: 28
26	Lambda	parameters: 35 body: 29
27	Literal
28	ExprTuple	31, 30
29	Conditional	value: 31 condition: 32
30	Variable
31	Operation	operator: 33 operands: 35
32	Operation	operator: 34 operands: 35
33	Variable
34	Variable
35	ExprTuple	36
36	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
37	Lambda	parameter: 43 body: 40
38	Literal
39	Variable
40	IndexedVar	variable: 41 index: 43
41	Variable
42	ExprTuple	43
43	Variable