Theorem or_if_any of type Forall

from the theory of proveit.logic.booleans.disjunction

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.disjunction import or_if_any

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

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