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
from proveit.logic import And, Equals, InSet
from proveit.numbers import Ceil, Floor, Real, Round, subtract

# build up the expression from sub-expressions
sub_expr1 = Ceil(x)
expr = Conditional(Equals(Round(x), sub_expr1), And(InSet(x, Real), Equals(subtract(x, Floor(x)), subtract(sub_expr1, x))))

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\{round\left(x\right) = \left\lceil x\right\rceil \textrm{ if } x \in \mathbb{R} ,  \left(x - \left\lfloor x\right\rfloor\right) = \left(\left\lceil x\right\rceil - x\right)\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: 12 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 21
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 9 operand: 29
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	Literal
10	Literal
11	ExprTuple	29, 14
12	Literal
13	ExprTuple	15, 16
14	Literal
15	Operation	operator: 18 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	29, 20
18	Literal
19	ExprTuple	21, 22
20	Operation	operator: 25 operand: 26
21	Operation	operator: 24 operand: 29
22	Operation	operator: 25 operand: 29
23	ExprTuple	26
24	Literal
25	Literal
26	Operation	operator: 27 operand: 29
27	Literal
28	ExprTuple	29
29	Variable