Expression of type ExprTuple

from the theory of proveit.logic.sets.comprehension

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
from proveit.core_expr_types import Q__x_1_to_n, R__x_1_to_n, S_1_to_n, f__x_1_to_n, x_1_to_n
from proveit.logic import Forall, SetOfAll, SubsetEq
from proveit.logic.sets import general_comprehension_fyn

# build up the expression from sub-expressions
sub_expr1 = [x_1_to_n]
sub_expr2 = [S_1_to_n]
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = Q__x_1_to_n, domains = sub_expr2, condition = R__x_1_to_n), SubsetEq(SetOfAll(instance_param_or_params = sub_expr1, instance_element = f__x_1_to_n, domains = sub_expr2, condition = R__x_1_to_n), general_comprehension_fyn).with_wrapping_at(2))

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_{\left(x_{1} \in S_{1}\right), \left(x_{2} \in S_{2}\right), \ldots, \left(x_{n} \in S_{n}\right)~|~R\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right), \begin{array}{c} \begin{array}{l} \left\{f\left(x_{1}, x_{2}, \ldots, x_{n}\right)~|~R\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right\}_{\left(x_{1} \in S_{1}\right), \left(x_{2} \in S_{2}\right), \ldots, \left(x_{n} \in S_{n}\right)} \subseteq  \\ \left\{f\left(y_{1}, y_{2}, \ldots, y_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right\}_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)} \end{array} \end{array}\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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameters: 33 body: 10
8	Operation	operator: 12 operand: 15
9	Operation	operator: 12 operand: 16
10	Conditional	value: 14 condition: 20
11	ExprTuple	15
12	Literal
13	ExprTuple	16
14	Operation	operator: 35 operands: 33
15	Lambda	parameters: 33 body: 17
16	Lambda	parameters: 36 body: 18
17	Conditional	value: 19 condition: 20
18	Conditional	value: 21 condition: 22
19	Operation	operator: 24 operands: 33
20	Operation	operator: 25 operands: 23
21	Operation	operator: 24 operands: 36
22	Operation	operator: 25 operands: 26
23	ExprTuple	27, 28
24	Variable
25	Literal
26	ExprTuple	29, 30
27	ExprRange	lambda_map: 31 start_index: 46 end_index: 47
28	Operation	operator: 32 operands: 33
29	ExprRange	lambda_map: 34 start_index: 46 end_index: 47
30	Operation	operator: 35 operands: 36
31	Lambda	parameter: 55 body: 37
32	Variable
33	ExprTuple	38
34	Lambda	parameter: 55 body: 39
35	Variable
36	ExprTuple	40
37	Operation	operator: 43 operands: 41
38	ExprRange	lambda_map: 42 start_index: 46 end_index: 47
39	Operation	operator: 43 operands: 44
40	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
41	ExprTuple	48, 49
42	Lambda	parameter: 55 body: 48
43	Literal
44	ExprTuple	50, 49
45	Lambda	parameter: 55 body: 50
46	Literal
47	Variable
48	IndexedVar	variable: 51 index: 55
49	IndexedVar	variable: 52 index: 55
50	IndexedVar	variable: 53 index: 55
51	Variable
52	Variable
53	Variable
54	ExprTuple	55
55	Variable