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, IndexedVar, Lambda, Variable, a, b, c, i, j, 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 Add, Complex, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, b_1_to_j, c_1_to_k], Conditional(Equals(Mult(a_1_to_i, Add(b_1_to_j), c_1_to_k), Add(ExprRange(sub_expr1, Mult(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j))).with_wrapping_at(2), And(ExprRange(sub_expr2, InSet(IndexedVar(a, sub_expr2), Complex), one, i), ExprRange(sub_expr2, InSet(IndexedVar(b, sub_expr2), Complex), one, j), ExprRange(sub_expr2, InSet(IndexedVar(c, sub_expr2), 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}, b_{1}, b_{2}, \ldots, b_{j}, 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(b_{1} +  b_{2} +  \ldots +  b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) =  \\ \left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{1}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{2}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \ldots +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{j}\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(b_{1} \in \mathbb{C}\right) ,  \left(b_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(b_{j} \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	40, 32, 42
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, 14
10	Operation	operator: 37 operands: 15
11	Operation	operator: 25 operands: 16
12	ExprRange	lambda_map: 17 start_index: 48 end_index: 44
13	ExprRange	lambda_map: 18 start_index: 48 end_index: 36
14	ExprRange	lambda_map: 19 start_index: 48 end_index: 49
15	ExprTuple	40, 20, 42
16	ExprTuple	21
17	Lambda	parameter: 56 body: 22
18	Lambda	parameter: 56 body: 23
19	Lambda	parameter: 56 body: 24
20	Operation	operator: 25 operands: 26
21	ExprRange	lambda_map: 27 start_index: 48 end_index: 36
22	Operation	operator: 30 operands: 28
23	Operation	operator: 30 operands: 29
24	Operation	operator: 30 operands: 31
25	Literal
26	ExprTuple	32
27	Lambda	parameter: 51 body: 33
28	ExprTuple	50, 34
29	ExprTuple	39, 34
30	Literal
31	ExprTuple	52, 34
32	ExprRange	lambda_map: 35 start_index: 48 end_index: 36
33	Operation	operator: 37 operands: 38
34	Literal
35	Lambda	parameter: 56 body: 39
36	Variable
37	Literal
38	ExprTuple	40, 41, 42
39	IndexedVar	variable: 45 index: 56
40	ExprRange	lambda_map: 43 start_index: 48 end_index: 44
41	IndexedVar	variable: 45 index: 51
42	ExprRange	lambda_map: 47 start_index: 48 end_index: 49
43	Lambda	parameter: 56 body: 50
44	Variable
45	Variable
46	ExprTuple	51
47	Lambda	parameter: 56 body: 52
48	Literal
49	Variable
50	IndexedVar	variable: 53 index: 56
51	Variable
52	IndexedVar	variable: 54 index: 56
53	Variable
54	Variable
55	ExprTuple	56
56	Variable