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 Implies, Not
from proveit.logic.booleans.quantification import general_exists_notPx_st_Qx, general_forall_Py_if_Qy

# build up the expression from sub-expressions
expr = Lambda([P, Q], Implies(general_exists_notPx_st_Qx, Not(general_forall_Py_if_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)}~(\lnot P\left(x_{1}, x_{2}, \ldots, x_{n}\right))\right] \Rightarrow  \\ (\lnot \left[\forall_{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	25, 26
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 18 operand: 11
7	Literal
8	ExprTuple	10
9	ExprTuple	11
10	Lambda	parameters: 24 body: 12
11	Operation	operator: 13 operand: 17
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	17
15	Operation	operator: 18 operand: 21
16	Operation	operator: 26 operands: 24
17	Lambda	parameters: 27 body: 20
18	Literal
19	ExprTuple	21
20	Conditional	value: 22 condition: 23
21	Operation	operator: 25 operands: 24
22	Operation	operator: 25 operands: 27
23	Operation	operator: 26 operands: 27
24	ExprTuple	28
25	Variable
26	Variable
27	ExprTuple	29
28	ExprRange	lambda_map: 30 start_index: 32 end_index: 33
29	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
30	Lambda	parameter: 39 body: 34
31	Lambda	parameter: 39 body: 35
32	Literal
33	Variable
34	IndexedVar	variable: 36 index: 39
35	IndexedVar	variable: 37 index: 39
36	Variable
37	Variable
38	ExprTuple	39
39	Variable