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 Conditional, ExprTuple, Lambda, Q, R, f, n
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, InSet, SetOfAll, SubsetEq
from proveit.logic.sets import general_comprehension_fyn
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
sub_expr1 = [x_1_to_n]
sub_expr2 = [S_1_to_n]
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [f, Q, R, S_1_to_n], instance_expr = 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)), 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, Q, R, S_{1}, S_{2}, \ldots, S_{n}}~\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) \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: 62 body: 3
2	ExprTuple	62
3	Conditional	value: 4 condition: 5
4	Operation	operator: 18 operand: 8
5	Operation	operator: 58 operands: 7
6	ExprTuple	8
7	ExprTuple	62, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	39, 50, 47, 12
11	Operation	operator: 13 operands: 14
12	ExprRange	lambda_map: 15 start_index: 61 end_index: 62
13	Literal
14	ExprTuple	16, 17
15	Lambda	parameter: 70 body: 64
16	Operation	operator: 18 operand: 22
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23, 24
22	Lambda	parameters: 48 body: 25
23	Operation	operator: 27 operand: 30
24	Operation	operator: 27 operand: 31
25	Conditional	value: 29 condition: 35
26	ExprTuple	30
27	Literal
28	ExprTuple	31
29	Operation	operator: 50 operands: 48
30	Lambda	parameters: 48 body: 32
31	Lambda	parameters: 51 body: 33
32	Conditional	value: 34 condition: 35
33	Conditional	value: 36 condition: 37
34	Operation	operator: 39 operands: 48
35	Operation	operator: 40 operands: 38
36	Operation	operator: 39 operands: 51
37	Operation	operator: 40 operands: 41
38	ExprTuple	42, 43
39	Variable
40	Literal
41	ExprTuple	44, 45
42	ExprRange	lambda_map: 46 start_index: 61 end_index: 62
43	Operation	operator: 47 operands: 48
44	ExprRange	lambda_map: 49 start_index: 61 end_index: 62
45	Operation	operator: 50 operands: 51
46	Lambda	parameter: 70 body: 52
47	Variable
48	ExprTuple	53
49	Lambda	parameter: 70 body: 54
50	Variable
51	ExprTuple	55
52	Operation	operator: 58 operands: 56
53	ExprRange	lambda_map: 57 start_index: 61 end_index: 62
54	Operation	operator: 58 operands: 59
55	ExprRange	lambda_map: 60 start_index: 61 end_index: 62
56	ExprTuple	63, 64
57	Lambda	parameter: 70 body: 63
58	Literal
59	ExprTuple	65, 64
60	Lambda	parameter: 70 body: 65
61	Literal
62	Variable
63	IndexedVar	variable: 66 index: 70
64	IndexedVar	variable: 67 index: 70
65	IndexedVar	variable: 68 index: 70
66	Variable
67	Variable
68	Variable
69	ExprTuple	70
70	Variable