Theorem demorgans_law_and_to_or 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 demorgans_law_and_to_or

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

Passed sanity check: demorgans_law_and_to_or matches stored_expr

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

\forall_{m \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{m}~|~\lnot \left((\lnot A_{1}) \land  (\lnot A_{2}) \land  \ldots \land  (\lnot A_{m})\right)}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\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	parameter: 27 body: 4
3	ExprTuple	27
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	27, 12
11	Lambda	parameters: 17 body: 13
12	Literal
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 29 operand: 20
16	Literal
17	ExprTuple	19
18	ExprTuple	20
19	ExprRange	lambda_map: 21 start_index: 26 end_index: 27
20	Operation	operator: 22 operands: 23
21	Lambda	parameter: 34 body: 31
22	Literal
23	ExprTuple	24
24	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
25	Lambda	parameter: 34 body: 28
26	Literal
27	Variable
28	Operation	operator: 29 operand: 31
29	Literal
30	ExprTuple	31
31	IndexedVar	variable: 32 index: 34
32	Variable
33	ExprTuple	34
34	Variable