Expression of type Lambda

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 Lambda, P, Q
from proveit.logic import Equals, Not
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy, general_notexists_Px_st_Qx

# build up the expression from sub-expressions
expr = Lambda([P, Q], Equals(general_notexists_Px_st_Qx, Not(general_exists_Py_st_Qy)).with_wrapping_at(2))

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, Q\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left[\nexists_{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)\right] =  \\ (\lnot \left[\exists_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right]) \end{array} \end{array}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	23, 24
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operand: 16
6	Operation	operator: 8 operand: 10
7	Literal
8	Literal
9	ExprTuple	10
10	Operation	operator: 12 operand: 16
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 23 operands: 17
15	Operation	operator: 24 operands: 17
16	Lambda	parameters: 25 body: 18
17	ExprTuple	19
18	Conditional	value: 20 condition: 21
19	ExprRange	lambda_map: 22 start_index: 30 end_index: 31
20	Operation	operator: 23 operands: 25
21	Operation	operator: 24 operands: 25
22	Lambda	parameter: 35 body: 26
23	Variable
24	Variable
25	ExprTuple	27
26	IndexedVar	variable: 28 index: 35
27	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
28	Variable
29	Lambda	parameter: 35 body: 32
30	Literal
31	Variable
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable