Expression of type ExprTuple

from the theory of proveit.numbers.integration

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, S
from proveit.core_expr_types import P__x_1_to_n, x_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import Integrate, Real

# build up the expression from sub-expressions
sub_expr1 = [x_1_to_n]
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(P__x_1_to_n, Real), domain = S), InSet(Integrate(index_or_indices = sub_expr1, integrand = P__x_1_to_n, domain = S), Real))

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_{x_{1}, x_{2}, \ldots, x_{n} \in S}~\left(P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \in \mathbb{R}\right), \left[\int_{x_{1}, x_{2}, \ldots, x_{n} \in S}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \in \mathbb{R}\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: 6
2	Operation	operator: 29 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 15
6	Lambda	parameters: 19 body: 8
7	Operation	operator: 9 operand: 12
8	Conditional	value: 11 condition: 17
9	Literal
10	ExprTuple	12
11	Operation	operator: 29 operands: 13
12	Lambda	parameters: 19 body: 14
13	ExprTuple	16, 15
14	Conditional	value: 16 condition: 17
15	Literal
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operands: 21
18	Variable
19	ExprTuple	22
20	Literal
21	ExprTuple	23
22	ExprRange	lambda_map: 24 start_index: 26 end_index: 27
23	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
24	Lambda	parameter: 35 body: 31
25	Lambda	parameter: 35 body: 28
26	Literal
27	Variable
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	IndexedVar	variable: 33 index: 35
32	Variable
33	Variable
34	ExprTuple	35
35	Variable