# 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, ExprTuple, 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 = ExprTuple(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(\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..\right)

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 27
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12
9Operationoperator: 26
operands: 13
10Operationoperator: 14
operands: 15
11Operationoperator: 17
operands: 16
12Operationoperator: 17
operands: 18
13ExprTuple28, 19
14Literal
15ExprTuple20, 21
16ExprTuple28, 22
17Literal
18ExprTuple29, 23
19Operationoperator: 24
operand: 29
20Literal
21Operationoperator: 26
operands: 27
22Literal
23Literal
24Literal
25ExprTuple29
26Literal
27ExprTuple28, 29
28Variable
29Variable