Expression of type Conditional

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, 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 = 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\{\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()

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: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 12 operand: 17
8	Operation	operator: 12 operand: 18
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	17
12	Literal
13	ExprTuple	18
14	ExprTuple	30, 19
15	Literal
16	ExprTuple	25, 20
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24, 26
22	Literal
23	ExprTuple	25, 26
24	Operation	operator: 27 operand: 30
25	Variable
26	Operation	operator: 28 operand: 30
27	Literal
28	Literal
29	ExprTuple	30
30	Variable