Theorem abs_ineq of type Forall

from the theory of proveit.numbers.absolute_value

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.absolute_value import abs_ineq

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

Passed sanity check: abs_ineq matches stored_expr

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

\forall_{x, y \in \mathbb{R}~|~y \geq 0}~\left(\left(\left|x\right| \leq y\right) \Leftrightarrow \left(\left(\left(-y\right) \leq x\right) \land \left(x \leq y\right)\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: 31 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 16 operands: 9
7	Literal
8	ExprTuple	10, 11
9	ExprTuple	12, 13, 14
10	Operation	operator: 30 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 19 operands: 18
13	Operation	operator: 19 operands: 20
14	Operation	operator: 30 operands: 21
15	ExprTuple	22, 36
16	Literal
17	ExprTuple	23, 24
18	ExprTuple	33, 25
19	Literal
20	ExprTuple	36, 25
21	ExprTuple	26, 36
22	Operation	operator: 27 operand: 33
23	Operation	operator: 30 operands: 29
24	Operation	operator: 30 operands: 31
25	Literal
26	Literal
27	Literal
28	ExprTuple	33
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	33, 36
32	Operation	operator: 34 operand: 36
33	Variable
34	Literal
35	ExprTuple	36
36	Variable