# 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, a, b, c, i, j, k
from proveit.logic import InSet
from proveit.numbers import Complex, one

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), Complex), one, 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())

\left(\left(a_{1} \in \mathbb{C}\right), \left(a_{2} \in \mathbb{C}\right), \ldots, \left(a_{i} \in \mathbb{C}\right),\left(b_{1} \in \mathbb{C}\right), \left(b_{2} \in \mathbb{C}\right), \ldots, \left(b_{j} \in \mathbb{C}\right),\left(c_{1} \in \mathbb{C}\right), \left(c_{2} \in \mathbb{C}\right), \ldots, \left(c_{k} \in \mathbb{C}\right)\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
1ExprRangelambda_map: 4
start_index: 9
end_index: 5
2ExprRangelambda_map: 6
start_index: 9
end_index: 7
3ExprRangelambda_map: 8
start_index: 9
end_index: 10
4Lambdaparameter: 26
body: 11
5Variable
6Lambdaparameter: 26
body: 12
7Variable
8Lambdaparameter: 26
body: 13
9Literal
10Variable
11Operationoperator: 16
operands: 14
12Operationoperator: 16
operands: 15
13Operationoperator: 16
operands: 17
14ExprTuple18, 21
15ExprTuple19, 21
16Literal
17ExprTuple20, 21
18IndexedVarvariable: 22
index: 26
19IndexedVarvariable: 23
index: 26
20IndexedVarvariable: 24
index: 26
21Literal
22Variable
23Variable
24Variable
25ExprTuple26
26Variable