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, fx, x
from proveit.logic import Forall, Implies, InSet
from proveit.numbers import Integrate, Real

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda([f, S], Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(fx, Real), domain = S), InSet(Integrate(index_or_indices = sub_expr1, integrand = fx, 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(\left(f, S\right) \mapsto \left(\left[\forall_{x \in S}~\left(f\left(x\right) \in \mathbb{R}\right)\right] \Rightarrow \left(\left[\int_{x \in S}~f\left(x\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, 28
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 25 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	12, 20
11	Lambda	parameter: 27 body: 13
12	Operation	operator: 14 operand: 17
13	Conditional	value: 16 condition: 22
14	Literal
15	ExprTuple	17
16	Operation	operator: 25 operands: 18
17	Lambda	parameter: 27 body: 19
18	ExprTuple	21, 20
19	Conditional	value: 21 condition: 22
20	Literal
21	Operation	operator: 23 operand: 27
22	Operation	operator: 25 operands: 26
23	Variable
24	ExprTuple	27
25	Literal
26	ExprTuple	27, 28
27	Variable
28	Variable