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 Conditional, ExprTuple, Lambda, S, f, n
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, NaturalPos, RealNonPos

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

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(n \mapsto \left\{\forall_{f, S}~\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}^{\le 0}\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}^{\le 0}\right)\right) \textrm{ if } n \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	parameter: 40 body: 3
2	ExprTuple	40
3	Conditional	value: 4 condition: 5
4	Operation	operator: 16 operand: 8
5	Operation	operator: 42 operands: 7
6	ExprTuple	8
7	ExprTuple	40, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	31, 45
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14, 15
14	Operation	operator: 16 operand: 19
15	Operation	operator: 42 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	20, 28
19	Lambda	parameters: 32 body: 21
20	Operation	operator: 22 operand: 25
21	Conditional	value: 24 condition: 30
22	Literal
23	ExprTuple	25
24	Operation	operator: 42 operands: 26
25	Lambda	parameters: 32 body: 27
26	ExprTuple	29, 28
27	Conditional	value: 29 condition: 30
28	Literal
29	Operation	operator: 31 operands: 32
30	Operation	operator: 33 operands: 34
31	Variable
32	ExprTuple	35
33	Literal
34	ExprTuple	36
35	ExprRange	lambda_map: 37 start_index: 39 end_index: 40
36	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
37	Lambda	parameter: 48 body: 44
38	Lambda	parameter: 48 body: 41
39	Literal
40	Variable
41	Operation	operator: 42 operands: 43
42	Literal
43	ExprTuple	44, 45
44	IndexedVar	variable: 46 index: 48
45	Variable
46	Variable
47	ExprTuple	48
48	Variable