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, ExprTuple, Lambda, c, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, d_1_to_k
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, Mult, Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j, k], Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c, d_1_to_k], instance_expr = Equals(Mult(a_1_to_i, b_1_to_j, c, d_1_to_k), Mult(a_1_to_i, c, b_1_to_j, d_1_to_k)).with_wrapping_at(2), domain = Complex), 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\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c, d_{1}, d_{2}, \ldots, d_{k} \in \mathbb{C}}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i}\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j} \cdot c\cdot d_{1} \cdot  d_{2} \cdot  \ldots \cdot  d_{k}\right) =  \\ \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot c\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\cdot d_{1} \cdot  d_{2} \cdot  \ldots \cdot  d_{k}\right) \end{array} \end{array}\right) \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	45, 47, 50
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 22 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 30 body: 13
10	Operation	operator: 53 operands: 14
11	Operation	operator: 53 operands: 15
12	Operation	operator: 53 operands: 16
13	Conditional	value: 17 condition: 18
14	ExprTuple	45, 19
15	ExprTuple	47, 19
16	ExprTuple	50, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27, 28, 29
24	Operation	operator: 31 operands: 30
25	Operation	operator: 31 operands: 32
26	ExprRange	lambda_map: 33 start_index: 49 end_index: 45
27	ExprRange	lambda_map: 34 start_index: 49 end_index: 47
28	Operation	operator: 53 operands: 35
29	ExprRange	lambda_map: 36 start_index: 49 end_index: 50
30	ExprTuple	37, 38, 42, 39
31	Literal
32	ExprTuple	37, 42, 38, 39
33	Lambda	parameter: 63 body: 40
34	Lambda	parameter: 63 body: 41
35	ExprTuple	42, 58
36	Lambda	parameter: 63 body: 43
37	ExprRange	lambda_map: 44 start_index: 49 end_index: 45
38	ExprRange	lambda_map: 46 start_index: 49 end_index: 47
39	ExprRange	lambda_map: 48 start_index: 49 end_index: 50
40	Operation	operator: 53 operands: 51
41	Operation	operator: 53 operands: 52
42	Variable
43	Operation	operator: 53 operands: 54
44	Lambda	parameter: 63 body: 55
45	Variable
46	Lambda	parameter: 63 body: 56
47	Variable
48	Lambda	parameter: 63 body: 57
49	Literal
50	Variable
51	ExprTuple	55, 58
52	ExprTuple	56, 58
53	Literal
54	ExprTuple	57, 58
55	IndexedVar	variable: 59 index: 63
56	IndexedVar	variable: 60 index: 63
57	IndexedVar	variable: 61 index: 63
58	Literal
59	Variable
60	Variable
61	Variable
62	ExprTuple	63
63	Variable