# from the theory of proveit.numbers.exponentiation¶

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, Variable, n, x
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, Exp, Mult, NaturalPos, one

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x], instance_expr = Equals(Mult(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), x, one, n)), Exp(x, n)), domain = Complex), domain = NaturalPos)

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())

\forall_{n \in \mathbb{N}^+}~\left[\forall_{x \in \mathbb{C}}~\left(\left(x \cdot  x \cdot  ..\left(n - 3\right) \times.. \cdot  x\right) = x^{n}\right)\right]

In [5]:
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 [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 30
body: 4
3ExprTuple30
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 18
operands: 9
7Literal
8ExprTuple10
9ExprTuple30, 11
10Lambdaparameter: 32
body: 13
11Literal
12ExprTuple32
13Conditionalvalue: 14
condition: 15
14Operationoperator: 16
operands: 17
15Operationoperator: 18
operands: 19
16Literal
17ExprTuple20, 21
18Literal
19ExprTuple32, 22
20Operationoperator: 23
operands: 24
21Operationoperator: 25
operands: 26
22Literal
23Literal
24ExprTuple27
25Literal
26ExprTuple32, 30
27ExprRangelambda_map: 28
start_index: 29
end_index: 30
28Lambdaparameter: 33
body: 32
29Literal
30Variable
31ExprTuple33
32Variable
33Variable