# 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, c, i, 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(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(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
1ExprRangelambda_map: 3
start_index: 6
end_index: 4
2ExprRangelambda_map: 5
start_index: 6
end_index: 7
3Lambdaparameter: 19
body: 8
4Variable
5Lambdaparameter: 19
body: 9
6Literal
7Variable
8Operationoperator: 11
operands: 10
9Operationoperator: 11
operands: 12
10ExprTuple13, 15
11Literal
12ExprTuple14, 15
13IndexedVarvariable: 16
index: 19
14IndexedVarvariable: 17
index: 19
15Literal
16Variable
17Variable
18ExprTuple19
19Variable