Theorem redundant_mod_elimination 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 redundant_mod_elimination

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

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