Expression of type ExprTuple

from the theory of proveit.numbers.summation

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 ExprTuple, Function, R, S, a, f, fa, fx, gy, x, y
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Sum

# build up the expression from sub-expressions
expr = ExprTuple(Forall(instance_param_or_params = [a], instance_expr = InSet(fa, Complex), domain = R), Equals(Sum(index_or_indices = [x], summand = fx, domain = R), Sum(index_or_indices = [y], summand = Function(f, [gy]), domain = S)))

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(\forall_{a \in R}~\left(f\left(a\right) \in \mathbb{C}\right), \left[\sum_{x \in R}~f\left(x\right)\right] = \left[\sum_{y \in S}~f\left(g\left(y\right)\right)\right]\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 35 body: 10
8	Operation	operator: 12 operand: 16
9	Operation	operator: 12 operand: 17
10	Conditional	value: 14 condition: 15
11	ExprTuple	16
12	Literal
13	ExprTuple	17
14	Operation	operator: 33 operands: 18
15	Operation	operator: 33 operands: 19
16	Lambda	parameter: 36 body: 20
17	Lambda	parameter: 42 body: 21
18	ExprTuple	22, 23
19	ExprTuple	35, 37
20	Conditional	value: 24 condition: 25
21	Conditional	value: 26 condition: 27
22	Operation	operator: 31 operand: 35
23	Literal
24	Operation	operator: 31 operand: 36
25	Operation	operator: 33 operands: 30
26	Operation	operator: 31 operand: 38
27	Operation	operator: 33 operands: 34
28	ExprTuple	35
29	ExprTuple	36
30	ExprTuple	36, 37
31	Variable
32	ExprTuple	38
33	Literal
34	ExprTuple	42, 39
35	Variable
36	Variable
37	Variable
38	Operation	operator: 40 operand: 42
39	Variable
40	Variable
41	ExprTuple	42
42	Variable