Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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