Expression of type Conditional

from the theory of proveit.numbers.exponentiation

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, a, b, n
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Exp, Mult, Neg, zero

# build up the expression from sub-expressions
expr = Conditional(Equals(Exp(Exp(a, Neg(b)), n), Exp(a, Neg(Mult(b, n)))), And(InSet(a, Complex), InSet(b, Complex), NotEquals(a, zero)))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{(a^{-b})^{n} = a^{-\left(b \cdot n\right)} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  a \neq 0\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 23 operands: 12
8	Operation	operator: 23 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 17 operands: 18
12	ExprTuple	19, 34
13	ExprTuple	26, 20
14	ExprTuple	26, 21
15	Literal
16	ExprTuple	33, 21
17	Literal
18	ExprTuple	26, 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 29 operand: 28
21	Literal
22	Literal
23	Literal
24	ExprTuple	26, 27
25	ExprTuple	28
26	Variable
27	Operation	operator: 29 operand: 33
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	33
31	Literal
32	ExprTuple	33, 34
33	Variable
34	Variable