# 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, IndexedVar, Variable, a, c, i, k
from proveit.logic import And, 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 = And(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(a_{1} \in \mathbb{C}\right) \land  \left(a_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(a_{i} \in \mathbb{C}\right)\land \left(c_{1} \in \mathbb{C}\right) \land  \left(c_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(c_{k} \in \mathbb{C}\right)

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
3ExprRangelambda_map: 5
start_index: 8
end_index: 6
4ExprRangelambda_map: 7
start_index: 8
end_index: 9
5Lambdaparameter: 21
body: 10
6Variable
7Lambdaparameter: 21
body: 11
8Literal
9Variable
10Operationoperator: 13
operands: 12
11Operationoperator: 13
operands: 14
12ExprTuple15, 17
13Literal
14ExprTuple16, 17
15IndexedVarvariable: 18
index: 21
16IndexedVarvariable: 19
index: 21
17Literal
18Variable
19Variable
20ExprTuple21
21Variable