# 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, 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 = 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(a, b\right) \mapsto \left\{\left(a \cdot b\right) \in \mathbb{N} \textrm{ if } a \in \mathbb{Z}^{-} ,  b \in \mathbb{Z}^{-}\right..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameters: 12
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 14
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple7, 8
5Literal
6ExprTuple9, 10
7Operationoperator: 11
operands: 12
8Literal
9Operationoperator: 14
operands: 13
10Operationoperator: 14
operands: 15
11Literal
12ExprTuple16, 17
13ExprTuple16, 18
14Literal
15ExprTuple17, 18
16Variable
17Variable
18Literal