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, e, l, t
from proveit.logic import Forall, InSet
from proveit.numbers import Exp, Integrate, IntervalCC, Real, frac, one, subtract, two

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, Exp(l, two))
sub_expr3 = IntervalCC(e, subtract(Exp(two, subtract(t, one)), one))
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr2, Real), domain = sub_expr3), InSet(Integrate(index_or_indices = sub_expr1, integrand = sub_expr2, domain = sub_expr3), 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_{l \in \left[e,2^{t - 1} - 1\right]}~\left(\frac{1}{l^{2}} \in \mathbb{R}\right), \left(\int_{e}^{2^{t - 1} - 1} \frac{1}{l^{2}}\,dl\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: 21 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 16
6	Lambda	parameter: 28 body: 8
7	Operation	operator: 9 operand: 12
8	Conditional	value: 11 condition: 18
9	Literal
10	ExprTuple	12
11	Operation	operator: 21 operands: 13
12	Lambda	parameter: 28 body: 15
13	ExprTuple	17, 16
14	ExprTuple	28
15	Conditional	value: 17 condition: 18
16	Literal
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	43, 23
21	Literal
22	ExprTuple	28, 24
23	Operation	operator: 33 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 35
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Variable
30	Operation	operator: 37 operands: 31
31	ExprTuple	32, 40
32	Operation	operator: 33 operands: 34
33	Literal
34	ExprTuple	35, 36
35	Literal
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Operation	operator: 41 operand: 43
41	Literal
42	ExprTuple	43
43	Literal