# 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 IndexedVar, Lambda, Variable, b
from proveit.core_expr_types import a_1_to_i, c_1_to_k
from proveit.numbers import Mult

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

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())

{_{-}b} \mapsto \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{{_{-}b}}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right)

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameter: 15
body: 1
1Operationoperator: 2
operands: 3
2Literal
3ExprTuple4, 5, 6
4ExprRangelambda_map: 7
start_index: 12
end_index: 8
5IndexedVarvariable: 9
index: 15
6ExprRangelambda_map: 11
start_index: 12
end_index: 13
7Lambdaparameter: 20
body: 14
8Variable
9Variable
10ExprTuple15
11Lambdaparameter: 20
body: 16
12Literal
13Variable
14IndexedVarvariable: 17
index: 20
15Variable
16IndexedVarvariable: 18
index: 20
17Variable
18Variable
19ExprTuple20
20Variable