# from the theory of proveit.numbers.ordering¶

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, b, c
from proveit.logic import And, InSet
from proveit.numbers import Add, Integer, Less, LessEq, Neg, one

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b, c], Conditional(LessEq(a, Add(b, c)), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), Less(a, b), LessEq(Neg(one), c)))))

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, b, c\right) \mapsto \left\{a \leq \left(b + c\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  a < b ,  \left(-1\right) \leq c\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
2ExprTuple26, 27, 29
3Conditionalvalue: 4
condition: 5
4Operationoperator: 23
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple26, 9
7Literal
8ExprTuple10, 11, 12, 13, 14
9Operationoperator: 15
operands: 16
10Operationoperator: 19
operands: 17
11Operationoperator: 19
operands: 18
12Operationoperator: 19
operands: 20
13Operationoperator: 21
operands: 22
14Operationoperator: 23
operands: 24
15Literal
16ExprTuple27, 29
17ExprTuple26, 25
18ExprTuple27, 25
19Literal
20ExprTuple29, 25
21Literal
22ExprTuple26, 27
23Literal
24ExprTuple28, 29
25Literal
26Variable
27Variable
28Operationoperator: 30
operand: 32
29Variable
30Literal
31ExprTuple32
32Literal