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, Lambda, Q, R, f
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, Implies, 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(Lambda([f, Q, R, S_1_to_n], Implies(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)).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(\left(f, Q, R, S_{1}, S_{2}, \ldots, S_{n}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \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)\right] \Rightarrow  \\ \left(\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) \end{array} \end{array}\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	31, 42, 39, 4
3	Operation	operator: 5 operands: 6
4	ExprRange	lambda_map: 7 start_index: 53 end_index: 54
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 62 body: 56
8	Operation	operator: 10 operand: 14
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	15, 16
14	Lambda	parameters: 40 body: 17
15	Operation	operator: 19 operand: 22
16	Operation	operator: 19 operand: 23
17	Conditional	value: 21 condition: 27
18	ExprTuple	22
19	Literal
20	ExprTuple	23
21	Operation	operator: 42 operands: 40
22	Lambda	parameters: 40 body: 24
23	Lambda	parameters: 43 body: 25
24	Conditional	value: 26 condition: 27
25	Conditional	value: 28 condition: 29
26	Operation	operator: 31 operands: 40
27	Operation	operator: 32 operands: 30
28	Operation	operator: 31 operands: 43
29	Operation	operator: 32 operands: 33
30	ExprTuple	34, 35
31	Variable
32	Literal
33	ExprTuple	36, 37
34	ExprRange	lambda_map: 38 start_index: 53 end_index: 54
35	Operation	operator: 39 operands: 40
36	ExprRange	lambda_map: 41 start_index: 53 end_index: 54
37	Operation	operator: 42 operands: 43
38	Lambda	parameter: 62 body: 44
39	Variable
40	ExprTuple	45
41	Lambda	parameter: 62 body: 46
42	Variable
43	ExprTuple	47
44	Operation	operator: 50 operands: 48
45	ExprRange	lambda_map: 49 start_index: 53 end_index: 54
46	Operation	operator: 50 operands: 51
47	ExprRange	lambda_map: 52 start_index: 53 end_index: 54
48	ExprTuple	55, 56
49	Lambda	parameter: 62 body: 55
50	Literal
51	ExprTuple	57, 56
52	Lambda	parameter: 62 body: 57
53	Literal
54	Variable
55	IndexedVar	variable: 58 index: 62
56	IndexedVar	variable: 59 index: 62
57	IndexedVar	variable: 60 index: 62
58	Variable
59	Variable
60	Variable
61	ExprTuple	62
62	Variable