Theorem 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 exists_folding

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

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