# from the theory of proveit.numbers.multiplication¶

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
from proveit.logic import And, InSet
from proveit.numbers import IntegerNeg, Mult, Natural

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b], Conditional(InSet(Mult(a, b), Natural), And(InSet(a, IntegerNeg), InSet(b, IntegerNeg)))))

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\right) \mapsto \left\{\left(a \cdot b\right) \in \mathbb{N} \textrm{ if } a \in \mathbb{Z}^{-} ,  b \in \mathbb{Z}^{-}\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: 13
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 15
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11
8Operationoperator: 12
operands: 13
9Literal
10Operationoperator: 15
operands: 14
11Operationoperator: 15
operands: 16
12Literal
13ExprTuple17, 18
14ExprTuple17, 19
15Literal
16ExprTuple18, 19
17Variable
18Variable
19Literal