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, Lambda, S, f
from proveit.core_expr_types import f__x_1_to_n, x_1_to_n
from proveit.logic import Forall, Implies, InSet
from proveit.numbers import Integrate, RealNeg

# build up the expression from sub-expressions
sub_expr1 = [x_1_to_n]
expr = ExprTuple(Lambda([f, S], Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(f__x_1_to_n, RealNeg), domain = S), InSet(Integrate(index_or_indices = sub_expr1, integrand = f__x_1_to_n, domain = S), RealNeg))))

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(f, S\right) \mapsto \left(\left[\forall_{x_{1}, x_{2}, \ldots, x_{n} \in S}~\left(f\left(x_{1}, x_{2}, \ldots, x_{n}\right) \in \mathbb{R}^-\right)\right] \Rightarrow \left(\left[\int_{x_{1}, x_{2}, \ldots, x_{n} \in S}~f\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \in \mathbb{R}^-\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	23, 37
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 34 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	12, 20
11	Lambda	parameters: 24 body: 13
12	Operation	operator: 14 operand: 17
13	Conditional	value: 16 condition: 22
14	Literal
15	ExprTuple	17
16	Operation	operator: 34 operands: 18
17	Lambda	parameters: 24 body: 19
18	ExprTuple	21, 20
19	Conditional	value: 21 condition: 22
20	Literal
21	Operation	operator: 23 operands: 24
22	Operation	operator: 25 operands: 26
23	Variable
24	ExprTuple	27
25	Literal
26	ExprTuple	28
27	ExprRange	lambda_map: 29 start_index: 31 end_index: 32
28	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
29	Lambda	parameter: 40 body: 36
30	Lambda	parameter: 40 body: 33
31	Literal
32	Variable
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	IndexedVar	variable: 38 index: 40
37	Variable
38	Variable
39	ExprTuple	40
40	Variable