# 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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, a, b
from proveit.logic import And, InSet
from proveit.numbers import Mult, RealNeg, RealPos

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

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 \cdot b\right) \in \mathbb{R}^- \textrm{ if } a \in \mathbb{R}^- ,  b \in \mathbb{R}^+\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 12
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 15
4Literal
5ExprTuple7, 8
6Operationoperator: 9
operands: 10
7Operationoperator: 12
operands: 11
8Operationoperator: 12
operands: 13
9Literal
10ExprTuple14, 16
11ExprTuple14, 15
12Literal
13ExprTuple16, 17
14Variable
15Literal
16Variable
17Literal