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
from proveit.core_expr_types import P__y_1_to_n, Q__y_1_to_n, y_1_to_n
from proveit.logic import And
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([y_1_to_n], Conditional(general_exists_Px_st_Qx, And(P__y_1_to_n, Q__y_1_to_n))))

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(y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{\exists_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } P\left(y_{1}, y_{2}, \ldots, y_{n}\right) ,  Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)\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: 13 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameters: 19 body: 12
10	Operation	operator: 17 operands: 13
11	Operation	operator: 18 operands: 13
12	Conditional	value: 14 condition: 15
13	ExprTuple	16
14	Operation	operator: 17 operands: 19
15	Operation	operator: 18 operands: 19
16	ExprRange	lambda_map: 20 start_index: 24 end_index: 25
17	Variable
18	Variable
19	ExprTuple	21
20	Lambda	parameter: 30 body: 22
21	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
22	IndexedVar	variable: 26 index: 30
23	Lambda	parameter: 30 body: 27
24	Literal
25	Variable
26	Variable
27	IndexedVar	variable: 28 index: 30
28	Variable
29	ExprTuple	30
30	Variable