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 ExprTuple, Lambda, P
from proveit.core_expr_types import P__y_1_to_n, y_1_to_n
from proveit.logic import Forall
from proveit.logic.booleans.quantification import general_exists_Px

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(P, Forall(instance_param_or_params = [y_1_to_n], instance_expr = general_exists_Px, condition = P__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(P \mapsto \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]\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: 17 body: 3
2	ExprTuple	17
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 12 body: 7
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 13
9	Operation	operator: 17 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	14
13	Lambda	parameters: 18 body: 15
14	ExprRange	lambda_map: 16 start_index: 23 end_index: 24
15	Operation	operator: 17 operands: 18
16	Lambda	parameter: 28 body: 19
17	Variable
18	ExprTuple	20
19	IndexedVar	variable: 21 index: 28
20	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
21	Variable
22	Lambda	parameter: 28 body: 25
23	Literal
24	Variable
25	IndexedVar	variable: 26 index: 28
26	Variable
27	ExprTuple	28
28	Variable