Expression of type ExprTuple

from the theory of proveit.logic.sets.intersection

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, n, x
from proveit.core_expr_types import Q__y_1_to_n, R__y_1_to_n, S_1_to_n, y_1_to_n
from proveit.logic import Equals, Exists, Forall, InSet
from proveit.logic.sets import general_intersectall_Ryn
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
sub_expr1 = [y_1_to_n]
sub_expr2 = [S_1_to_n]
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [S_1_to_n, Q, R, x], instance_expr = Equals(InSet(x, general_intersectall_Ryn), Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(x, R__y_1_to_n), domains = sub_expr2, condition = Q__y_1_to_n)).with_wrapping_at(1), condition = Exists(instance_param_or_params = sub_expr1, instance_expr = Q__y_1_to_n, domains = sub_expr2)), 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_{S_{1}, S_{2}, \ldots, S_{n}, Q, R, x~|~\exists_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)}~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(\begin{array}{c} \begin{array}{l} \left(x \in \left[\bigcap_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~R\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right]\right) \\  = \left[\forall_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(x \in R\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right)\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: 55 body: 3
2	ExprTuple	55
3	Conditional	value: 4 condition: 5
4	Operation	operator: 24 operand: 8
5	Operation	operator: 51 operands: 7
6	ExprTuple	8
7	ExprTuple	55, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	12, 47, 43, 39
11	Conditional	value: 13 condition: 14
12	ExprRange	lambda_map: 15 start_index: 54 end_index: 55
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operand: 22
15	Lambda	parameter: 61 body: 56
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22
20	Operation	operator: 51 operands: 23
21	Operation	operator: 24 operand: 28
22	Lambda	parameters: 48 body: 26
23	ExprTuple	39, 27
24	Literal
25	ExprTuple	28
26	Conditional	value: 45 condition: 29
27	Operation	operator: 30 operand: 34
28	Lambda	parameters: 48 body: 32
29	Operation	operator: 41 operands: 33
30	Literal
31	ExprTuple	34
32	Conditional	value: 35 condition: 38
33	ExprTuple	44
34	Lambda	parameters: 48 body: 36
35	Operation	operator: 51 operands: 37
36	Conditional	value: 40 condition: 38
37	ExprTuple	39, 40
38	Operation	operator: 41 operands: 42
39	Variable
40	Operation	operator: 43 operands: 48
41	Literal
42	ExprTuple	44, 45
43	Variable
44	ExprRange	lambda_map: 46 start_index: 54 end_index: 55
45	Operation	operator: 47 operands: 48
46	Lambda	parameter: 61 body: 49
47	Variable
48	ExprTuple	50
49	Operation	operator: 51 operands: 52
50	ExprRange	lambda_map: 53 start_index: 54 end_index: 55
51	Literal
52	ExprTuple	57, 56
53	Lambda	parameter: 61 body: 57
54	Literal
55	Variable
56	IndexedVar	variable: 58 index: 61
57	IndexedVar	variable: 59 index: 61
58	Variable
59	Variable
60	ExprTuple	61
61	Variable