Expression of type ExprTuple

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, ExprTuple, Function, IndexedVar, Lambda, 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 = ExprTuple(Lambda([a_1_to_i, c_1_to_k], 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(\left(a_{1}, a_{2}, \ldots, a_{i}, c_{1}, c_{2}, \ldots, c_{k}\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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