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

# build up the expression from sub-expressions
expr = Conditional(Equals(Exp(a, Neg(n)), frac(one, Exp(a, n))), And(InSet(a, ComplexNonZero), InSet(n, NaturalPos)))

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^{-n} = \frac{1}{a^{n}} \textrm{ if } a \in \mathbb{C}^{\neq 0} ,  n \in \mathbb{N}^+\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
7	Operation	operator: 24 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	26, 17
12	Literal
13	ExprTuple	18, 19
14	ExprTuple	26, 20
15	Literal
16	ExprTuple	27, 21
17	Operation	operator: 22 operand: 27
18	Literal
19	Operation	operator: 24 operands: 25
20	Literal
21	Literal
22	Literal
23	ExprTuple	27
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Variable