Expression of type Lambda

from the theory of proveit.numbers.rounding

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, InSet
from proveit.numbers import Abs, Integer, LessEq, Real, Round, subtract

# build up the expression from sub-expressions
expr = Lambda([x, y], Conditional(LessEq(Abs(subtract(Round(x), x)), Abs(subtract(y, x))), And(InSet(x, Real), InSet(y, Integer))))

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|round\left(x\right) - x\right| \leq \left|y - x\right| \textrm{ if } x \in \mathbb{R} ,  y \in \mathbb{Z}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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