Expression of type Conditional

from the theory of proveit.numbers.absolute_value

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, x, y
from proveit.logic import And, Iff, InSet
from proveit.numbers import Abs, LessEq, Neg, Real, greater_eq, zero

# build up the expression from sub-expressions
expr = Conditional(Iff(LessEq(Abs(x), y), And(LessEq(Neg(y), x), LessEq(x, y))), And(InSet(x, Real), InSet(y, Real), greater_eq(y, zero)))

expr:

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

Passed sanity check: expr matches stored_expr

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

\left\{\left(\left|x\right| \leq y\right) \Leftrightarrow \left(\left(\left(-y\right) \leq x\right) \land \left(x \leq y\right)\right) \textrm{ if } x \in \mathbb{R} ,  y \in \mathbb{R} ,  y \geq 0\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 12 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	8, 9, 10
6	Operation	operator: 26 operands: 11
7	Operation	operator: 12 operands: 13
8	Operation	operator: 15 operands: 14
9	Operation	operator: 15 operands: 16
10	Operation	operator: 26 operands: 17
11	ExprTuple	18, 32
12	Literal
13	ExprTuple	19, 20
14	ExprTuple	29, 21
15	Literal
16	ExprTuple	32, 21
17	ExprTuple	22, 32
18	Operation	operator: 23 operand: 29
19	Operation	operator: 26 operands: 25
20	Operation	operator: 26 operands: 27
21	Literal
22	Literal
23	Literal
24	ExprTuple	29
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	29, 32
28	Operation	operator: 30 operand: 32
29	Variable
30	Literal
31	ExprTuple	32
32	Variable