Theorem disassociation of type Forall

from the theory of proveit.logic.booleans.conjunction

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.conjunction import disassociation

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

Passed sanity check: disassociation matches stored_expr

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

\forall_{l, m, n \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land \left(B_{1} \land  B_{2} \land  \ldots \land  B_{m}\right)\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) =  \\ \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\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	parameters: 3 body: 4
3	ExprTuple	43, 56, 45
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 40 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12, 13
10	Lambda	parameters: 30 body: 14
11	Operation	operator: 48 operands: 15
12	Operation	operator: 48 operands: 16
13	Operation	operator: 48 operands: 17
14	Conditional	value: 18 condition: 19
15	ExprTuple	43, 20
16	ExprTuple	56, 20
17	ExprTuple	45, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 40 operands: 23
20	Literal
21	Literal
22	ExprTuple	24, 25
23	ExprTuple	26, 27, 28
24	Operation	operator: 40 operands: 29
25	Operation	operator: 40 operands: 30
26	ExprRange	lambda_map: 31 start_index: 55 end_index: 43
27	ExprRange	lambda_map: 32 start_index: 55 end_index: 56
28	ExprRange	lambda_map: 33 start_index: 55 end_index: 45
29	ExprTuple	35, 34, 36
30	ExprTuple	35, 50, 36
31	Lambda	parameter: 62 body: 37
32	Lambda	parameter: 62 body: 38
33	Lambda	parameter: 62 body: 39
34	Operation	operator: 40 operands: 41
35	ExprRange	lambda_map: 42 start_index: 55 end_index: 43
36	ExprRange	lambda_map: 44 start_index: 55 end_index: 45
37	Operation	operator: 48 operands: 46
38	Operation	operator: 48 operands: 47
39	Operation	operator: 48 operands: 49
40	Literal
41	ExprTuple	50
42	Lambda	parameter: 62 body: 51
43	Variable
44	Lambda	parameter: 62 body: 52
45	Variable
46	ExprTuple	51, 53
47	ExprTuple	59, 53
48	Literal
49	ExprTuple	52, 53
50	ExprRange	lambda_map: 54 start_index: 55 end_index: 56
51	IndexedVar	variable: 57 index: 62
52	IndexedVar	variable: 58 index: 62
53	Literal
54	Lambda	parameter: 62 body: 59
55	Literal
56	Variable
57	Variable
58	Variable
59	IndexedVar	variable: 60 index: 62
60	Variable
61	ExprTuple	62
62	Variable