# 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 ExprTuple, i, j, k
from proveit.logic import InSet
from proveit.numbers import Natural, NaturalPos

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(InSet(i, Natural), InSet(j, NaturalPos), InSet(k, 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(i \in \mathbb{N}, j \in \mathbb{N}^+, k \in \mathbb{N}\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2, 3
1Operationoperator: 6
operands: 4
2Operationoperator: 6
operands: 5
3Operationoperator: 6
operands: 7
4ExprTuple8, 12
5ExprTuple9, 10
6Literal
7ExprTuple11, 12
8Variable
9Variable
10Literal
11Variable
12Literal