# from the theory of proveit.numbers.multiplication¶

see dependencies

In [1]:
import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import the special expression
from proveit.numbers.multiplication import mult_neg_any_double

In [2]:
# check that the built expression is the same as the stored expression
assert mult_neg_any_double.expr == stored_expr
assert mult_neg_any_double.expr._style_id == stored_expr._style_id
print("Passed sanity check: mult_neg_any_double matches stored_expr")

Passed sanity check: mult_neg_any_double matches stored_expr

In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{i, j \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{C}}~\left(\left(-\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left(-b\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j}\right)\right) = \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j}\right)\right)\right]

In [4]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [5]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple46, 51
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 21
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12
10Lambdaparameters: 29
body: 13
11Operationoperator: 39
operands: 14
12Operationoperator: 39
operands: 15
13Conditionalvalue: 16
condition: 17
14ExprTuple46, 18
15ExprTuple51, 18
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operands: 22
18Literal
19Literal
20ExprTuple23, 24
21Literal
22ExprTuple25, 26, 27
23Operationoperator: 47
operand: 33
24Operationoperator: 36
operands: 29
25ExprRangelambda_map: 30
start_index: 50
end_index: 46
26Operationoperator: 39
operands: 31
27ExprRangelambda_map: 32
start_index: 50
end_index: 51
28ExprTuple33
29ExprTuple41, 53, 43
30Lambdaparameter: 58
body: 34
31ExprTuple53, 44
32Lambdaparameter: 58
body: 35
33Operationoperator: 36
operands: 37
34Operationoperator: 39
operands: 38
35Operationoperator: 39
operands: 40
36Literal
37ExprTuple41, 42, 43
38ExprTuple52, 44
39Literal
40ExprTuple54, 44
41ExprRangelambda_map: 45
start_index: 50
end_index: 46
42Operationoperator: 47
operand: 53
43ExprRangelambda_map: 49
start_index: 50
end_index: 51
44Literal
45Lambdaparameter: 58
body: 52
46Variable
47Literal
48ExprTuple53
49Lambdaparameter: 58
body: 54
50Literal
51Variable
52IndexedVarvariable: 55
index: 58
53Variable
54IndexedVarvariable: 56
index: 58
55Variable
56Variable
57ExprTuple58
58Variable