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
from proveit.logic.booleans.quantification import general_forall__Py_not_T__st_Qy, general_notexists_Px_st_Qx

# build up the expression from sub-expressions
expr = Lambda([P, Q], Equals(general_notexists_Px_st_Qx, general_forall__Py_not_T__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] =  \\ \left[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(P\left(y_{1}, y_{2}, \ldots, y_{n}\right) \neq \top\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	27, 22
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operand: 12
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12
11	Lambda	parameters: 19 body: 13
12	Lambda	parameters: 28 body: 14
13	Conditional	value: 15 condition: 16
14	Conditional	value: 17 condition: 18
15	Operation	operator: 27 operands: 19
16	Operation	operator: 22 operands: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 28
19	ExprTuple	23
20	Literal
21	ExprTuple	24, 25
22	Variable
23	ExprRange	lambda_map: 26 start_index: 33 end_index: 34
24	Operation	operator: 27 operands: 28
25	Literal
26	Lambda	parameter: 38 body: 29
27	Variable
28	ExprTuple	30
29	IndexedVar	variable: 31 index: 38
30	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
31	Variable
32	Lambda	parameter: 38 body: 35
33	Literal
34	Variable
35	IndexedVar	variable: 36 index: 38
36	Variable
37	ExprTuple	38
38	Variable