# 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, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import Mult, Natural, RationalNonNeg

In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(Mult(a_1_to_n), RationalNonNeg), domain = RationalNonNeg), InSet(n, Natural))

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\{\forall_{a_{1}, a_{2}, \ldots, a_{n} \in \mathbb{Q}^{\geq 0}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \in \mathbb{Q}^{\geq 0}\right) \textrm{ if } n \in \mathbb{N}\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: 3
operand: 6
2Operationoperator: 24
operands: 5
3Literal
4ExprTuple6
5ExprTuple23, 7
6Lambdaparameters: 17
body: 8
7Literal
8Conditionalvalue: 9
condition: 10
9Operationoperator: 24
operands: 11
10Operationoperator: 12
operands: 13
11ExprTuple14, 27
12Literal
13ExprTuple15
14Operationoperator: 16
operands: 17
15ExprRangelambda_map: 18
start_index: 22
end_index: 23
16Literal
17ExprTuple19
18Lambdaparameter: 30
body: 20
19ExprRangelambda_map: 21
start_index: 22
end_index: 23
20Operationoperator: 24
operands: 25
21Lambdaparameter: 30
body: 26
22Literal
23Variable
24Literal
25ExprTuple26, 27
26IndexedVarvariable: 28
index: 30
27Literal
28Variable
29ExprTuple30
30Variable