# 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 elim_one_any

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

Passed sanity check: elim_one_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_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot 1\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right) = \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i}\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{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
3ExprTuple37, 40
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 21
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12
10Lambdaparameters: 29
body: 13
11Operationoperator: 42
operands: 14
12Operationoperator: 42
operands: 15
13Conditionalvalue: 16
condition: 17
14ExprTuple37, 18
15ExprTuple40, 18
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operands: 22
18Literal
19Literal
20ExprTuple23, 24
21Literal
22ExprTuple25, 26
23Operationoperator: 28
operands: 27
24Operationoperator: 28
operands: 29
25ExprRangelambda_map: 30
start_index: 39
end_index: 37
26ExprRangelambda_map: 31
start_index: 39
end_index: 40
27ExprTuple32, 39, 33
28Literal
29ExprTuple32, 33
30Lambdaparameter: 50
body: 34
31Lambdaparameter: 50
body: 35
32ExprRangelambda_map: 36
start_index: 39
end_index: 37
33ExprRangelambda_map: 38
start_index: 39
end_index: 40
34Operationoperator: 42
operands: 41
35Operationoperator: 42
operands: 43
36Lambdaparameter: 50
body: 44
37Variable
38Lambdaparameter: 50
body: 45
39Literal
40Variable
41ExprTuple44, 46
42Literal
43ExprTuple45, 46
44IndexedVarvariable: 47
index: 50
45IndexedVarvariable: 48
index: 50
46Literal
47Variable
48Variable
49ExprTuple50
50Variable