# from the theory of proveit.numbers.rounding¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import x
from proveit.logic import Equals, Forall
from proveit.numbers import Ceil, Floor, Real, Round, subtract

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Ceil(x)
expr = Forall(instance_param_or_params = [x], instance_expr = Equals(Round(x), sub_expr1), domain = Real, condition = Equals(subtract(x, Floor(x)), subtract(sub_expr1, x)))

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{x \in \mathbb{R}~|~\left(x - \left\lfloor x\right\rfloor\right) = \left(\left\lceil x\right\rceil - x\right)}~\left(round\left(x\right) = \left\lceil x\right\rceil\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameter: 33
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 16
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 25
8Literal
9ExprTuple11, 12
10Operationoperator: 13
operand: 33
11Operationoperator: 14
operands: 15
12Operationoperator: 16
operands: 17
13Literal
14Literal
15ExprTuple33, 18
16Literal
17ExprTuple19, 20
18Literal
19Operationoperator: 22
operands: 21
20Operationoperator: 22
operands: 23
21ExprTuple33, 24
22Literal
23ExprTuple25, 26
24Operationoperator: 29
operand: 30
25Operationoperator: 28
operand: 33
26Operationoperator: 29
operand: 33
27ExprTuple30
28Literal
29Literal
30Operationoperator: 31
operand: 33
31Literal
32ExprTuple33
33Variable