# 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 ExprRange, ExprTuple, IndexedVar, Variable, b, j
from proveit.core_expr_types import a_1_to_i, c_1_to_k
from proveit.numbers import Mult, one

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
expr = ExprTuple(ExprRange(sub_expr1, Mult(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j))

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_{i} \cdot b_{1}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right), \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{2}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right), \ldots, \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{j}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\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
1ExprRangelambda_map: 2
start_index: 15
end_index: 3
2Lambdaparameter: 18
body: 4
3Variable
4Operationoperator: 5
operands: 6
5Literal
6ExprTuple7, 8, 9
7ExprRangelambda_map: 10
start_index: 15
end_index: 11
8IndexedVarvariable: 12
index: 18
9ExprRangelambda_map: 14
start_index: 15
end_index: 16
10Lambdaparameter: 23
body: 17
11Variable
12Variable
13ExprTuple18
14Lambdaparameter: 23
body: 19
15Literal
16Variable
17IndexedVarvariable: 20
index: 23
18Variable
19IndexedVarvariable: 21
index: 23
20Variable
21Variable
22ExprTuple23
23Variable