Theorem exists_not_implies_not_forall 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 exists_not_implies_not_forall

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

Passed sanity check: exists_not_implies_not_forall 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} \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)\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: 24 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 44 body: 4
3	ExprTuple	44
4	Conditional	value: 5 condition: 6
5	Operation	operator: 24 operand: 10
6	Operation	operator: 8 operands: 9
7	ExprTuple	10
8	Literal
9	ExprTuple	44, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	36, 37
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 18 operand: 21
17	Operation	operator: 29 operand: 22
18	Literal
19	ExprTuple	21
20	ExprTuple	22
21	Lambda	parameters: 35 body: 23
22	Operation	operator: 24 operand: 28
23	Conditional	value: 26 condition: 27
24	Literal
25	ExprTuple	28
26	Operation	operator: 29 operand: 32
27	Operation	operator: 37 operands: 35
28	Lambda	parameters: 38 body: 31
29	Literal
30	ExprTuple	32
31	Conditional	value: 33 condition: 34
32	Operation	operator: 36 operands: 35
33	Operation	operator: 36 operands: 38
34	Operation	operator: 37 operands: 38
35	ExprTuple	39
36	Variable
37	Variable
38	ExprTuple	40
39	ExprRange	lambda_map: 41 start_index: 43 end_index: 44
40	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
41	Lambda	parameter: 50 body: 45
42	Lambda	parameter: 50 body: 46
43	Literal
44	Variable
45	IndexedVar	variable: 47 index: 50
46	IndexedVar	variable: 48 index: 50
47	Variable
48	Variable
49	ExprTuple	50
50	Variable