Expression of type ExprTuple

from the theory of proveit.numbers.addition

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, 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, 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_1_to_k], instance_expr = Equals(Add(a_1_to_i, b_1_to_j, c_1_to_k), Add(a_1_to_i, Add(b_1_to_j), c_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_{1}, c_{2}, \ldots, c_{k} \in \mathbb{C}}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j}+ c_{1} +  c_{2} +  \ldots +  c_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i} + \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right)+ c_{1} +  c_{2} +  \ldots +  c_{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	41, 56, 45
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: 29 body: 13
10	Operation	operator: 48 operands: 14
11	Operation	operator: 48 operands: 15
12	Operation	operator: 48 operands: 16
13	Conditional	value: 17 condition: 18
14	ExprTuple	41, 19
15	ExprTuple	56, 19
16	ExprTuple	45, 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
24	Operation	operator: 42 operands: 29
25	Operation	operator: 42 operands: 30
26	ExprRange	lambda_map: 31 start_index: 55 end_index: 41
27	ExprRange	lambda_map: 32 start_index: 55 end_index: 56
28	ExprRange	lambda_map: 33 start_index: 55 end_index: 45
29	ExprTuple	34, 50, 36
30	ExprTuple	34, 35, 36
31	Lambda	parameter: 62 body: 37
32	Lambda	parameter: 62 body: 38
33	Lambda	parameter: 62 body: 39
34	ExprRange	lambda_map: 40 start_index: 55 end_index: 41
35	Operation	operator: 42 operands: 43
36	ExprRange	lambda_map: 44 start_index: 55 end_index: 45
37	Operation	operator: 48 operands: 46
38	Operation	operator: 48 operands: 47
39	Operation	operator: 48 operands: 49
40	Lambda	parameter: 62 body: 51
41	Variable
42	Literal
43	ExprTuple	50
44	Lambda	parameter: 62 body: 52
45	Variable
46	ExprTuple	51, 53
47	ExprTuple	59, 53
48	Literal
49	ExprTuple	52, 53
50	ExprRange	lambda_map: 54 start_index: 55 end_index: 56
51	IndexedVar	variable: 57 index: 62
52	IndexedVar	variable: 58 index: 62
53	Literal
54	Lambda	parameter: 62 body: 59
55	Literal
56	Variable
57	Variable
58	Variable
59	IndexedVar	variable: 60 index: 62
60	Variable
61	ExprTuple	62
62	Variable