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Expression of type ExprTuple

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, ExprTuple, Lambda, x
from proveit.logic import Equals, InSet
from proveit.numbers import Ceil, Real, Round, frac, one, subtract, two
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(x, Conditional(Equals(Round(x), Ceil(subtract(x, frac(one, two)))), 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(x \mapsto \left\{round\left(x\right) = \left\lceil x - \frac{1}{2}\right\rceil \textrm{ if } x \in \mathbb{R}\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 19
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple19, 11
9Operationoperator: 12
operand: 19
10Operationoperator: 14
operand: 16
11Literal
12Literal
13ExprTuple19
14Literal
15ExprTuple16
16Operationoperator: 17
operands: 18
17Literal
18ExprTuple19, 20
19Variable
20Operationoperator: 21
operand: 23
21Literal
22ExprTuple23
23Operationoperator: 24
operands: 25
24Literal
25ExprTuple26, 27
26Literal
27Literal