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 Conditional, Lambda, P, Q
from proveit.logic import Not
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx, general_forall__Py_not_T__st_Qy

# build up the expression from sub-expressions
expr = Lambda([P, Q], Conditional(general_exists_Px_st_Qx, Not(general_forall__Py_not_T__st_Qy)))

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\{\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 } \lnot \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]\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	30, 25
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operand: 10
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10
9	Lambda	parameters: 17 body: 11
10	Operation	operator: 12 operand: 16
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 30 operands: 17
15	Operation	operator: 25 operands: 17
16	Lambda	parameters: 31 body: 18
17	ExprTuple	19
18	Conditional	value: 20 condition: 21
19	ExprRange	lambda_map: 22 start_index: 34 end_index: 35
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 31
22	Lambda	parameter: 39 body: 26
23	Literal
24	ExprTuple	27, 28
25	Variable
26	IndexedVar	variable: 29 index: 39
27	Operation	operator: 30 operands: 31
28	Literal
29	Variable
30	Variable
31	ExprTuple	32
32	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
33	Lambda	parameter: 39 body: 36
34	Literal
35	Variable
36	IndexedVar	variable: 37 index: 39
37	Variable
38	ExprTuple	39
39	Variable