# 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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, 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 = 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(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..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple23, 25, 26
2Conditionalvalue: 3
condition: 4
3Operationoperator: 21
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11, 12, 13
8Operationoperator: 15
operands: 14
9Operationoperator: 15
operands: 16
10Operationoperator: 19
operands: 17
11Operationoperator: 19
operands: 18
12Operationoperator: 19
operands: 20
13Operationoperator: 21
operands: 22
14ExprTuple25, 23
15Literal
16ExprTuple26, 23
17ExprTuple23, 24
18ExprTuple25, 24
19Literal
20ExprTuple26, 24
21Literal
22ExprTuple25, 26
23Variable
24Literal
25Variable
26Variable