Expression of type ExprTuple

from the theory of proveit.logic.booleans.quantification.existence

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, P, n
from proveit.core_expr_types import P__y_1_to_n, y_1_to_n
from proveit.logic import Forall, InSet
from proveit.logic.booleans.quantification import general_exists_Px
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [P], instance_expr = Forall(instance_param_or_params = [y_1_to_n], instance_expr = general_exists_Px, condition = P__y_1_to_n)), 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_{P}~\left[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left[\exists_{x_{1}, x_{2}, \ldots, x_{n}}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right]\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: 33 body: 3
2	ExprTuple	33
3	Conditional	value: 4 condition: 5
4	Operation	operator: 13 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	33, 10
9	Lambda	parameter: 26 body: 12
10	Literal
11	ExprTuple	26
12	Operation	operator: 13 operand: 15
13	Literal
14	ExprTuple	15
15	Lambda	parameters: 21 body: 16
16	Conditional	value: 17 condition: 18
17	Operation	operator: 19 operand: 22
18	Operation	operator: 26 operands: 21
19	Literal
20	ExprTuple	22
21	ExprTuple	23
22	Lambda	parameters: 27 body: 24
23	ExprRange	lambda_map: 25 start_index: 32 end_index: 33
24	Operation	operator: 26 operands: 27
25	Lambda	parameter: 37 body: 28
26	Variable
27	ExprTuple	29
28	IndexedVar	variable: 30 index: 37
29	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
30	Variable
31	Lambda	parameter: 37 body: 34
32	Literal
33	Variable
34	IndexedVar	variable: 35 index: 37
35	Variable
36	ExprTuple	37
37	Variable