Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([x, y], 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(x, y\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 29 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 14 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	10, 11, 12
8	Operation	operator: 28 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 17 operands: 16
11	Operation	operator: 17 operands: 18
12	Operation	operator: 28 operands: 19
13	ExprTuple	20, 34
14	Literal
15	ExprTuple	21, 22
16	ExprTuple	31, 23
17	Literal
18	ExprTuple	34, 23
19	ExprTuple	24, 34
20	Operation	operator: 25 operand: 31
21	Operation	operator: 28 operands: 27
22	Operation	operator: 28 operands: 29
23	Literal
24	Literal
25	Literal
26	ExprTuple	31
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	31, 34
30	Operation	operator: 32 operand: 34
31	Variable
32	Literal
33	ExprTuple	34
34	Variable