# 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, ExprTuple, IndexedVar, Lambda, 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 = ExprTuple(Lambda([a_1_to_n], 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}, a_{2}, \ldots, a_{n}\right) \mapsto \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..\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: 11
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 18
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 21
6Literal
7ExprTuple9
8Operationoperator: 10
operands: 11
9ExprRangelambda_map: 12
start_index: 16
end_index: 17
10Literal
11ExprTuple13
12Lambdaparameter: 24
body: 14
13ExprRangelambda_map: 15
start_index: 16
end_index: 17
14Operationoperator: 18
operands: 19
15Lambdaparameter: 24
body: 20
16Literal
17Variable
18Literal
19ExprTuple20, 21
20IndexedVarvariable: 22
index: 24
21Literal
22Variable
23ExprTuple24
24Variable