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Expression of type Conditional

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.
%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, Forall, InSet
from proveit.numbers import Add, Integer, Real, Round
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [n], instance_expr = Equals(Round(Add(x, n)), Add(Round(x), n)), domain = Integer), InSet(x, Real))
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())
\left\{\forall_{n \in \mathbb{Z}}~\left(round\left(x + n\right) = \left(round\left(x\right) + n\right)\right) \textrm{ if } x \in \mathbb{R}\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 6
2Operationoperator: 14
operands: 5
3Literal
4ExprTuple6
5ExprTuple28, 7
6Lambdaparameter: 27
body: 9
7Literal
8ExprTuple27
9Conditionalvalue: 10
condition: 11
10Operationoperator: 12
operands: 13
11Operationoperator: 14
operands: 15
12Literal
13ExprTuple16, 17
14Literal
15ExprTuple27, 18
16Operationoperator: 25
operand: 21
17Operationoperator: 23
operands: 20
18Literal
19ExprTuple21
20ExprTuple22, 27
21Operationoperator: 23
operands: 24
22Operationoperator: 25
operand: 28
23Literal
24ExprTuple28, 27
25Literal
26ExprTuple28
27Variable
28Variable