Theorem mod_real_closure 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_real_closure

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

Passed sanity check: mod_real_closure 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}~|~b \neq 0}~\left(\left(a ~\textup{mod}~ b\right) \in \mathbb{R}\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: 15 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 17 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 22
8	Literal
9	ExprTuple	11, 12, 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	Operation	operator: 19 operands: 20
14	Literal
15	ExprTuple	21, 23
16	ExprTuple	21, 22
17	Literal
18	ExprTuple	23, 22
19	Literal
20	ExprTuple	23, 24
21	Variable
22	Literal
23	Variable
24	Literal