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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, n, x
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Ceil, Integer, Real
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(x, Conditional(Forall(instance_param_or_params = [n], instance_expr = Equals(Ceil(Add(x, n)), Add(Ceil(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(x \mapsto \left\{\forall_{n \in \mathbb{Z}}~\left(\left\lceil x + n\right\rceil = \left(\left\lceil x\right\rceil + n\right)\right) \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: 30
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 16
operands: 7
5Literal
6ExprTuple8
7ExprTuple30, 9
8Lambdaparameter: 29
body: 11
9Literal
10ExprTuple29
11Conditionalvalue: 12
condition: 13
12Operationoperator: 14
operands: 15
13Operationoperator: 16
operands: 17
14Literal
15ExprTuple18, 19
16Literal
17ExprTuple29, 20
18Operationoperator: 27
operand: 23
19Operationoperator: 25
operands: 22
20Literal
21ExprTuple23
22ExprTuple24, 29
23Operationoperator: 25
operands: 26
24Operationoperator: 27
operand: 30
25Literal
26ExprTuple30, 29
27Literal
28ExprTuple30
29Variable
30Variable