# 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 Conditional, Lambda, a, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import ComplexNonZero, Exp, NaturalPos, Neg, frac, one

In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, n], Conditional(Equals(Exp(a, Neg(n)), frac(one, Exp(a, n))), And(InSet(a, ComplexNonZero), InSet(n, 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())

\left(a, n\right) \mapsto \left\{a^{-n} = \frac{1}{a^{n}} \textrm{ if } a \in \mathbb{C}^{\neq 0} ,  n \in \mathbb{N}^+\right..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameters: 26
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple10, 11
8Operationoperator: 25
operands: 12
9Operationoperator: 13
operands: 14
10Operationoperator: 16
operands: 15
11Operationoperator: 16
operands: 17
12ExprTuple27, 18
13Literal
14ExprTuple19, 20
15ExprTuple27, 21
16Literal
17ExprTuple28, 22
18Operationoperator: 23
operand: 28
19Literal
20Operationoperator: 25
operands: 26
21Literal
22Literal
23Literal
24ExprTuple28
25Literal
26ExprTuple27, 28
27Variable
28Variable