Theorem mod_abs_diff_reversal 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_abs_diff_reversal

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

Passed sanity check: mod_abs_diff_reversal matches stored_expr

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

\forall_{a \in \mathbb{R}, b \in \mathbb{R}, N \in \mathbb{R}^+}~\left(\left|a - b\right|_{\textup{mod}\thinspace N} = \left|b - a\right|_{\textup{mod}\thinspace N}\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: 4 body: 5
4	ExprTuple	38, 37, 27
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	Operation	operator: 22 operands: 20
15	Operation	operator: 22 operands: 21
16	Operation	operator: 22 operands: 23
17	ExprTuple	24, 27
18	Literal
19	ExprTuple	25, 27
20	ExprTuple	38, 26
21	ExprTuple	37, 26
22	Literal
23	ExprTuple	27, 28
24	Operation	operator: 30 operands: 29
25	Operation	operator: 30 operands: 31
26	Literal
27	Variable
28	Literal
29	ExprTuple	38, 32
30	Literal
31	ExprTuple	37, 33
32	Operation	operator: 35 operand: 37
33	Operation	operator: 35 operand: 38
34	ExprTuple	37
35	Literal
36	ExprTuple	38
37	Variable
38	Variable