Theorem not_exists_folding of type Forall

from the theory of proveit.logic.booleans.quantification.existence

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.logic.booleans.quantification.existence import not_exists_folding

# check that the built expression is the same as the stored expression
assert not_exists_folding.expr == stored_expr
assert not_exists_folding.expr._style_id == stored_expr._style_id
print("Passed sanity check: not_exists_folding matches stored_expr")

Passed sanity check: not_exists_folding matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{n \in \mathbb{N}^+}~\left[\forall_{P, Q}~\left(\begin{array}{c} \begin{array}{l} (\lnot \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]) \Rightarrow  \\ \left[\nexists_{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)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 42 body: 4
3	ExprTuple	42
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	42, 12
11	Lambda	parameters: 13 body: 14
12	Literal
13	ExprTuple	34, 35
14	Operation	operator: 15 operands: 16
15	Literal
16	ExprTuple	17, 18
17	Operation	operator: 19 operand: 22
18	Operation	operator: 21 operand: 26
19	Literal
20	ExprTuple	22
21	Literal
22	Operation	operator: 23 operand: 26
23	Literal
24	ExprTuple	26
25	Conditional	value: 27 condition: 28
26	Lambda	parameters: 36 body: 29
27	Operation	operator: 34 operands: 30
28	Operation	operator: 35 operands: 30
29	Conditional	value: 31 condition: 32
30	ExprTuple	33
31	Operation	operator: 34 operands: 36
32	Operation	operator: 35 operands: 36
33	ExprRange	lambda_map: 37 start_index: 41 end_index: 42
34	Variable
35	Variable
36	ExprTuple	38
37	Lambda	parameter: 47 body: 39
38	ExprRange	lambda_map: 40 start_index: 41 end_index: 42
39	IndexedVar	variable: 43 index: 47
40	Lambda	parameter: 47 body: 44
41	Literal
42	Variable
43	Variable
44	IndexedVar	variable: 45 index: 47
45	Variable
46	ExprTuple	47
47	Variable