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_Px_st_Qx, general_forall__Py_not_T__st_Qy

# build up the expression from sub-expressions
expr = Lambda([P, Q], Equals(general_exists_Px_st_Qx, Not(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[\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)\right] =  \\ (\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]) \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	32, 27
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	Operation	operator: 14 operand: 18
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	18
16	Operation	operator: 32 operands: 19
17	Operation	operator: 27 operands: 19
18	Lambda	parameters: 33 body: 20
19	ExprTuple	21
20	Conditional	value: 22 condition: 23
21	ExprRange	lambda_map: 24 start_index: 36 end_index: 37
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 33
24	Lambda	parameter: 41 body: 28
25	Literal
26	ExprTuple	29, 30
27	Variable
28	IndexedVar	variable: 31 index: 41
29	Operation	operator: 32 operands: 33
30	Literal
31	Variable
32	Variable
33	ExprTuple	34
34	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
35	Lambda	parameter: 41 body: 38
36	Literal
37	Variable
38	IndexedVar	variable: 39 index: 41
39	Variable
40	ExprTuple	41
41	Variable