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, Function, K, V, c, k
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.logic import Equals, Implies, InSet
from proveit.numbers import Mult

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
sub_expr2 = Function(c, sub_expr1)
sub_expr3 = VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, f__b_1_to_j), condition = Q__b_1_to_j)
expr = Conditional(Implies(InSet(sub_expr3, V), Equals(ScalarMult(k, sub_expr3), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(k, sub_expr2), f__b_1_to_j), condition = Q__b_1_to_j)).with_wrapping_at(1)).with_wrapping_at(1), InSet(k, 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}{c} \begin{array}{l} \left(\left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(c\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right] \in V\right) \\  \Rightarrow \left(\begin{array}{c} \begin{array}{l} \left(k \cdot \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(c\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right]\right) \\  = \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(\left(k \cdot c\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right] \end{array} \end{array}\right) \end{array} \end{array} \textrm{ if } k \in K\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	36, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 11 operands: 12
8	Variable
9	Literal
10	ExprTuple	18, 13
11	Literal
12	ExprTuple	14, 15
13	Variable
14	Operation	operator: 30 operands: 16
15	Operation	operator: 20 operand: 19
16	ExprTuple	36, 18
17	ExprTuple	19
18	Operation	operator: 20 operand: 23
19	Lambda	parameters: 40 body: 22
20	Literal
21	ExprTuple	23
22	Conditional	value: 24 condition: 28
23	Lambda	parameters: 40 body: 25
24	Operation	operator: 30 operands: 26
25	Conditional	value: 27 condition: 28
26	ExprTuple	29, 35
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 40
29	Operation	operator: 33 operands: 34
30	Literal
31	ExprTuple	37, 35
32	Variable
33	Literal
34	ExprTuple	36, 37
35	Operation	operator: 38 operands: 40
36	Variable
37	Operation	operator: 39 operands: 40
38	Variable
39	Variable
40	ExprTuple	41
41	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
42	Lambda	parameter: 48 body: 45
43	Literal
44	Variable
45	IndexedVar	variable: 46 index: 48
46	Variable
47	ExprTuple	48
48	Variable