Expression of type Equals

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 x, y
from proveit.logic import Equals
from proveit.numbers import Add, Ceil, Neg, two

# build up the expression from sub-expressions
sub_expr1 = Add(Neg(y), two)
expr = Equals(Ceil(Add(x, sub_expr1)), Add(Ceil(x), sub_expr1))

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\lceil x + \left(-y + 2\right)\right\rceil = \left(\left\lceil x\right\rceil + \left(-y + 2\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 10 operand: 7
4	Operation	operator: 14 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 12
7	Operation	operator: 14 operands: 9
8	Operation	operator: 10 operand: 13
9	ExprTuple	13, 12
10	Literal
11	ExprTuple	13
12	Operation	operator: 14 operands: 15
13	Variable
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 18 operand: 20
17	Literal
18	Literal
19	ExprTuple	20
20	Variable