# 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

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

Passed sanity check: mult_neg_any 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(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) = \left(-\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)\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
3ExprTuple49, 52
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 21
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12
10Lambdaparameters: 40
body: 13
11Operationoperator: 42
operands: 14
12Operationoperator: 42
operands: 15
13Conditionalvalue: 16
condition: 17
14ExprTuple49, 18
15ExprTuple52, 18
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operands: 22
18Literal
19Literal
20ExprTuple23, 24
21Literal
22ExprTuple25, 26, 27
23Operationoperator: 39
operands: 28
24Operationoperator: 37
operand: 34
25ExprRangelambda_map: 30
start_index: 51
end_index: 49
26Operationoperator: 42
operands: 31
27ExprRangelambda_map: 32
start_index: 51
end_index: 52
28ExprTuple44, 33, 46
29ExprTuple34
30Lambdaparameter: 58
body: 35
31ExprTuple45, 47
32Lambdaparameter: 58
body: 36
33Operationoperator: 37
operand: 45
34Operationoperator: 39
operands: 40
35Operationoperator: 42
operands: 41
36Operationoperator: 42
operands: 43
37Literal
38ExprTuple45
39Literal
40ExprTuple44, 45, 46
41ExprTuple53, 47
42Literal
43ExprTuple54, 47
44ExprRangelambda_map: 48
start_index: 51
end_index: 49
45Variable
46ExprRangelambda_map: 50
start_index: 51
end_index: 52
47Literal
48Lambdaparameter: 58
body: 53
49Variable
50Lambdaparameter: 58
body: 54
51Literal
52Variable
53IndexedVarvariable: 55
index: 58
54IndexedVarvariable: 56
index: 58
55Variable
56Variable
57ExprTuple58
58Variable