# 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 Function, f
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.numbers import Mult

In [2]:
# build up the expression from sub-expressions
expr = Mult(a_1_to_i, Function(f, [b_1_to_j]), 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())

a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4, 5
3ExprRangelambda_map: 6
start_index: 17
end_index: 7
4Operationoperator: 8
operands: 9
5ExprRangelambda_map: 10
start_index: 17
end_index: 11
6Lambdaparameter: 23
body: 12
7Variable
8Variable
9ExprTuple13
10Lambdaparameter: 23
body: 14
11Variable
12IndexedVarvariable: 15
index: 23
13ExprRangelambda_map: 16
start_index: 17
end_index: 18
14IndexedVarvariable: 19
index: 23
15Variable
16Lambdaparameter: 23
body: 20
17Literal
18Variable
19Variable
20IndexedVarvariable: 21
index: 23
21Variable
22ExprTuple23
23Variable