Theorem unbundle of type Forall

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

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.universality import unbundle

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

Passed sanity check: unbundle matches stored_expr

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

\forall_{m, n \in \mathbb{N}^+}~\left[\forall_{P, Q, R}~\left(\begin{array}{c} \begin{array}{l} \left[\forall_{x_{1}, x_{2}, \ldots, x_{m}, y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{m}\right), R\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)\right] \\  \Rightarrow \left[\forall_{x_{1}, x_{2}, \ldots, x_{m}~|~Q\left(x_{1}, x_{2}, \ldots, x_{m}\right)}~\left[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~R\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)\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: 32 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	48, 51
4	Conditional	value: 5 condition: 6
5	Operation	operator: 32 operand: 9
6	Operation	operator: 30 operands: 8
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	42, 36, 43
13	Operation	operator: 17 operands: 18
14	ExprTuple	48, 19
15	Literal
16	ExprTuple	51, 19
17	Literal
18	ExprTuple	20, 21
19	Literal
20	Operation	operator: 32 operand: 24
21	Operation	operator: 32 operand: 25
22	ExprTuple	24
23	ExprTuple	25
24	Lambda	parameters: 44 body: 26
25	Lambda	parameters: 37 body: 27
26	Conditional	value: 40 condition: 28
27	Conditional	value: 29 condition: 34
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operand: 35
30	Literal
31	ExprTuple	34, 41
32	Literal
33	ExprTuple	35
34	Operation	operator: 36 operands: 37
35	Lambda	parameters: 38 body: 39
36	Variable
37	ExprTuple	45
38	ExprTuple	46
39	Conditional	value: 40 condition: 41
40	Operation	operator: 42 operands: 44
41	Operation	operator: 43 operands: 44
42	Variable
43	Variable
44	ExprTuple	45, 46
45	ExprRange	lambda_map: 47 start_index: 50 end_index: 48
46	ExprRange	lambda_map: 49 start_index: 50 end_index: 51
47	Lambda	parameter: 57 body: 52
48	Variable
49	Lambda	parameter: 57 body: 53
50	Literal
51	Variable
52	IndexedVar	variable: 54 index: 57
53	IndexedVar	variable: 55 index: 57
54	Variable
55	Variable
56	ExprTuple	57
57	Variable