Theorem mod_in_zero_set of type Forall

from the theory of proveit.numbers.modular

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.numbers.modular import mod_in_zero_set

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

Passed sanity check: mod_in_zero_set matches stored_expr

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

\forall_{a, b \in \mathbb{R}~|~a = 0}~\left(\left(a ~\textup{mod}~ b\right) \in \left\{0\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 16 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 20 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 17 operand: 27
12	Operation	operator: 20 operands: 19
13	Operation	operator: 20 operands: 21
14	Operation	operator: 22 operands: 23
15	Literal
16	ExprTuple	26, 24
17	Literal
18	ExprTuple	27
19	ExprTuple	26, 25
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27
24	Variable
25	Literal
26	Variable
27	Literal