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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, y
from proveit.logic import And, InSet
from proveit.numbers import Add, Ceil, Real, greater_eq, one, subtract
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, y], Conditional(greater_eq(Ceil(Add(x, y)), subtract(Add(Ceil(x), Ceil(y)), one)), And(InSet(x, Real), InSet(y, 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(\left(x, y\right) \mapsto \left\{\left\lceil x + y\right\rceil \geq \left(\left(\left\lceil x\right\rceil + \left\lceil y\right\rceil\right) - 1\right) \textrm{ if } x \in \mathbb{R} ,  y \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
1Lambdaparameters: 26
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12
9Operationoperator: 25
operands: 13
10Operationoperator: 31
operand: 20
11Operationoperator: 16
operands: 15
12Operationoperator: 16
operands: 17
13ExprTuple18, 19
14ExprTuple20
15ExprTuple33, 21
16Literal
17ExprTuple34, 21
18Operationoperator: 25
operands: 22
19Operationoperator: 23
operand: 29
20Operationoperator: 25
operands: 26
21Literal
22ExprTuple27, 28
23Literal
24ExprTuple29
25Literal
26ExprTuple33, 34
27Operationoperator: 31
operand: 33
28Operationoperator: 31
operand: 34
29Literal
30ExprTuple33
31Literal
32ExprTuple34
33Variable
34Variable