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, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, a, b, c, d, e, 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, InSet
from proveit.numbers import Add, Complex, Neg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, b, c_1_to_j, d, e_1_to_k], Conditional(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)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), InSet(b, Complex), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), Complex), one, j), InSet(d, Complex), ExprRange(sub_expr1, InSet(IndexedVar(e, sub_expr1), 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, c_{1}, c_{2}, \ldots, c_{j}, d, e_{1}, e_{2}, \ldots, e_{k}\right) \mapsto \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) \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{C}\right) ,  b \in \mathbb{C}, \left(c_{1} \in \mathbb{C}\right) ,  \left(c_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(c_{j} \in \mathbb{C}\right) ,  d \in \mathbb{C}, \left(e_{1} \in \mathbb{C}\right) ,  \left(e_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(e_{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	26, 46, 27, 31, 28
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, 15, 16
10	Operation	operator: 18 operands: 17
11	Operation	operator: 18 operands: 19
12	ExprRange	lambda_map: 20 start_index: 40 end_index: 36
13	Operation	operator: 44 operands: 21
14	ExprRange	lambda_map: 22 start_index: 40 end_index: 38
15	Operation	operator: 44 operands: 23
16	ExprRange	lambda_map: 24 start_index: 40 end_index: 41
17	ExprTuple	26, 25, 27, 31, 28
18	Literal
19	ExprTuple	26, 27, 28
20	Lambda	parameter: 55 body: 29
21	ExprTuple	46, 50
22	Lambda	parameter: 55 body: 30
23	ExprTuple	31, 50
24	Lambda	parameter: 55 body: 32
25	Operation	operator: 33 operand: 46
26	ExprRange	lambda_map: 35 start_index: 40 end_index: 36
27	ExprRange	lambda_map: 37 start_index: 40 end_index: 38
28	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
29	Operation	operator: 44 operands: 42
30	Operation	operator: 44 operands: 43
31	Variable
32	Operation	operator: 44 operands: 45
33	Literal
34	ExprTuple	46
35	Lambda	parameter: 55 body: 47
36	Variable
37	Lambda	parameter: 55 body: 48
38	Variable
39	Lambda	parameter: 55 body: 49
40	Literal
41	Variable
42	ExprTuple	47, 50
43	ExprTuple	48, 50
44	Literal
45	ExprTuple	49, 50
46	Variable
47	IndexedVar	variable: 51 index: 55
48	IndexedVar	variable: 52 index: 55
49	IndexedVar	variable: 53 index: 55
50	Literal
51	Variable
52	Variable
53	Variable
54	ExprTuple	55
55	Variable