Expression of type ExprTuple

from the theory of proveit.numbers.addition.subtraction

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, b, d, i, j, k
from proveit.core_expr_types import a_1_to_i, c_1_to_j, e_1_to_k
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Complex, Natural, Neg

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j, k], Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j, d, e_1_to_k], instance_expr = Equals(Add(a_1_to_i, Neg(b), c_1_to_j, d, e_1_to_k), Add(a_1_to_i, c_1_to_j, e_1_to_k)), 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, c_{1}, c_{2}, \ldots, c_{j}, d, e_{1}, e_{2}, \ldots, e_{k} \in \mathbb{C}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} - b+ c_{1} +  c_{2} +  \ldots +  c_{j} + d+ e_{1} +  e_{2} +  \ldots +  e_{k}\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ c_{1} +  c_{2} +  \ldots +  c_{j}+ e_{1} +  e_{2} +  \ldots +  e_{k}\right)\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	51, 53, 56
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: 59 operands: 15
11	Operation	operator: 59 operands: 16
12	Operation	operator: 59 operands: 17
13	ExprTuple	41, 61, 42, 46, 43
14	Conditional	value: 18 condition: 19
15	ExprTuple	51, 20
16	ExprTuple	53, 20
17	ExprTuple	56, 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, 30, 31
25	Operation	operator: 33 operands: 32
26	Operation	operator: 33 operands: 34
27	ExprRange	lambda_map: 35 start_index: 55 end_index: 51
28	Operation	operator: 59 operands: 36
29	ExprRange	lambda_map: 37 start_index: 55 end_index: 53
30	Operation	operator: 59 operands: 38
31	ExprRange	lambda_map: 39 start_index: 55 end_index: 56
32	ExprTuple	41, 40, 42, 46, 43
33	Literal
34	ExprTuple	41, 42, 43
35	Lambda	parameter: 70 body: 44
36	ExprTuple	61, 65
37	Lambda	parameter: 70 body: 45
38	ExprTuple	46, 65
39	Lambda	parameter: 70 body: 47
40	Operation	operator: 48 operand: 61
41	ExprRange	lambda_map: 50 start_index: 55 end_index: 51
42	ExprRange	lambda_map: 52 start_index: 55 end_index: 53
43	ExprRange	lambda_map: 54 start_index: 55 end_index: 56
44	Operation	operator: 59 operands: 57
45	Operation	operator: 59 operands: 58
46	Variable
47	Operation	operator: 59 operands: 60
48	Literal
49	ExprTuple	61
50	Lambda	parameter: 70 body: 62
51	Variable
52	Lambda	parameter: 70 body: 63
53	Variable
54	Lambda	parameter: 70 body: 64
55	Literal
56	Variable
57	ExprTuple	62, 65
58	ExprTuple	63, 65
59	Literal
60	ExprTuple	64, 65
61	Variable
62	IndexedVar	variable: 66 index: 70
63	IndexedVar	variable: 67 index: 70
64	IndexedVar	variable: 68 index: 70
65	Literal
66	Variable
67	Variable
68	Variable
69	ExprTuple	70
70	Variable