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, b, 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, Forall, InSet
from proveit.numbers import Add, Complex, Mult, Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
expr = ExprTuple(Lambda([i, j, k], Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c_1_to_k], instance_expr = 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), domain = Complex).with_wrapping(), And(InSet(i, Natural), InSet(j, Natural), InSet(k, Natural)))))

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(i, j, k\right) \mapsto \left\{\begin{array}{l}\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k} \in \mathbb{C}}~\\
\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}\right)\end{array} \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \in \mathbb{N}\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	59, 51, 64
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 23 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 13 body: 14
10	Operation	operator: 45 operands: 15
11	Operation	operator: 45 operands: 16
12	Operation	operator: 45 operands: 17
13	ExprTuple	55, 47, 57
14	Conditional	value: 18 condition: 19
15	ExprTuple	59, 20
16	ExprTuple	51, 20
17	ExprTuple	64, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Literal
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28, 29
25	Operation	operator: 52 operands: 30
26	Operation	operator: 40 operands: 31
27	ExprRange	lambda_map: 32 start_index: 63 end_index: 59
28	ExprRange	lambda_map: 33 start_index: 63 end_index: 51
29	ExprRange	lambda_map: 34 start_index: 63 end_index: 64
30	ExprTuple	55, 35, 57
31	ExprTuple	36
32	Lambda	parameter: 71 body: 37
33	Lambda	parameter: 71 body: 38
34	Lambda	parameter: 71 body: 39
35	Operation	operator: 40 operands: 41
36	ExprRange	lambda_map: 42 start_index: 63 end_index: 51
37	Operation	operator: 45 operands: 43
38	Operation	operator: 45 operands: 44
39	Operation	operator: 45 operands: 46
40	Literal
41	ExprTuple	47
42	Lambda	parameter: 66 body: 48
43	ExprTuple	65, 49
44	ExprTuple	54, 49
45	Literal
46	ExprTuple	67, 49
47	ExprRange	lambda_map: 50 start_index: 63 end_index: 51
48	Operation	operator: 52 operands: 53
49	Literal
50	Lambda	parameter: 71 body: 54
51	Variable
52	Literal
53	ExprTuple	55, 56, 57
54	IndexedVar	variable: 60 index: 71
55	ExprRange	lambda_map: 58 start_index: 63 end_index: 59
56	IndexedVar	variable: 60 index: 66
57	ExprRange	lambda_map: 62 start_index: 63 end_index: 64
58	Lambda	parameter: 71 body: 65
59	Variable
60	Variable
61	ExprTuple	66
62	Lambda	parameter: 71 body: 67
63	Literal
64	Variable
65	IndexedVar	variable: 68 index: 71
66	Variable
67	IndexedVar	variable: 69 index: 71
68	Variable
69	Variable
70	ExprTuple	71
71	Variable