# from the theory of proveit.numbers.addition¶

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 Conditional, ExprTuple, Lambda, a, x, y
from proveit.logic import And, InSet
from proveit.numbers import Add, LessEq, Real

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, x, y], Conditional(LessEq(Add(x, a), Add(y, a)), And(InSet(a, Real), InSet(x, Real), InSet(y, Real), LessEq(x, y)))))

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(a, x, y\right) \mapsto \left\{\left(x + a\right) \leq \left(y + a\right) \textrm{ if } a \in \mathbb{R} ,  x \in \mathbb{R} ,  y \in \mathbb{R} ,  x \leq y\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: 2
body: 3
2ExprTuple24, 26, 27
3Conditionalvalue: 4
condition: 5
4Operationoperator: 22
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13, 14
9Operationoperator: 16
operands: 15
10Operationoperator: 16
operands: 17
11Operationoperator: 20
operands: 18
12Operationoperator: 20
operands: 19
13Operationoperator: 20
operands: 21
14Operationoperator: 22
operands: 23
15ExprTuple26, 24
16Literal
17ExprTuple27, 24
18ExprTuple24, 25
19ExprTuple26, 25
20Literal
21ExprTuple27, 25
22Literal
23ExprTuple26, 27
24Variable
25Literal
26Variable
27Variable