Expression of type Conditional

from the theory of proveit.numbers.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, ExprRange, Function, IndexedVar, Q, Variable, a, c, f, i, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Mult, Sum, one
from proveit.numbers.summation import summation_b1toj_fQ

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [b_1_to_j]
expr = Conditional(Equals(Mult(a_1_to_i, summation_b1toj_fQ, c_1_to_k), Sum(index_or_indices = sub_expr2, summand = Mult(a_1_to_i, Function(f, sub_expr2), c_1_to_k), condition = Function(Q, sub_expr2))).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), Complex), one, 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(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \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 c_{1} \cdot  c_{2} \cdot  \ldots \cdot  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} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right)\right] \end{array} \end{array} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{C}\right), \left(c_{1} \in \mathbb{C}\right) ,  \left(c_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(c_{k} \in \mathbb{C}\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: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 29 operands: 11
8	Operation	operator: 19 operand: 16
9	ExprRange	lambda_map: 13 start_index: 47 end_index: 37
10	ExprRange	lambda_map: 14 start_index: 47 end_index: 41
11	ExprTuple	32, 15, 34
12	ExprTuple	16
13	Lambda	parameter: 53 body: 17
14	Lambda	parameter: 53 body: 18
15	Operation	operator: 19 operand: 25
16	Lambda	parameters: 39 body: 21
17	Operation	operator: 23 operands: 22
18	Operation	operator: 23 operands: 24
19	Literal
20	ExprTuple	25
21	Conditional	value: 26 condition: 31
22	ExprTuple	42, 27
23	Literal
24	ExprTuple	44, 27
25	Lambda	parameters: 39 body: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	Conditional	value: 33 condition: 31
29	Literal
30	ExprTuple	32, 33, 34
31	Operation	operator: 35 operands: 39
32	ExprRange	lambda_map: 36 start_index: 47 end_index: 37
33	Operation	operator: 38 operands: 39
34	ExprRange	lambda_map: 40 start_index: 47 end_index: 41
35	Variable
36	Lambda	parameter: 53 body: 42
37	Variable
38	Variable
39	ExprTuple	43
40	Lambda	parameter: 53 body: 44
41	Variable
42	IndexedVar	variable: 45 index: 53
43	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
44	IndexedVar	variable: 49 index: 53
45	Variable
46	Lambda	parameter: 53 body: 50
47	Literal
48	Variable
49	Variable
50	IndexedVar	variable: 51 index: 53
51	Variable
52	ExprTuple	53
53	Variable