# 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, ExprRange, IndexedVar, Variable, a, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import Mult, RationalNonNeg, one

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(InSet(Mult(a_1_to_n), RationalNonNeg), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), RationalNonNeg), one, n)))

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_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \in \mathbb{Q}^{\geq 0} \textrm{ if } \left(a_{1} \in \mathbb{Q}^{\geq 0}\right) \land  \left(a_{2} \in \mathbb{Q}^{\geq 0}\right) \land  \ldots \land  \left(a_{n} \in \mathbb{Q}^{\geq 0}\right)\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: 16
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 19
4Literal
5ExprTuple7
6Operationoperator: 8
operands: 9
7ExprRangelambda_map: 10
start_index: 14
end_index: 15
8Literal
9ExprTuple11
10Lambdaparameter: 22
body: 12
11ExprRangelambda_map: 13
start_index: 14
end_index: 15
12Operationoperator: 16
operands: 17
13Lambdaparameter: 22
body: 18
14Literal
15Variable
16Literal
17ExprTuple18, 19
18IndexedVarvariable: 20
index: 22
19Literal
20Variable
21ExprTuple22
22Variable