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, n, x
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Ceil, Integer

# build up the expression from sub-expressions
expr = Conditional(Equals(Ceil(Add(x, n)), Add(Ceil(x), n)), InSet(n, 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\lceil x + n\right\rceil = \left(\left\lceil x\right\rceil + n\right) \textrm{ if } n \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	18, 9
7	Operation	operator: 16 operand: 12
8	Operation	operator: 14 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	13, 18
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operand: 19
14	Literal
15	ExprTuple	19, 18
16	Literal
17	ExprTuple	19
18	Variable
19	Variable