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, n, x
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, Mult, Natural, Neg, two

# build up the expression from sub-expressions
sub_expr1 = Mult(two, n)
expr = Conditional(Equals(Exp(x, sub_expr1), Exp(Neg(x), sub_expr1)), InSet(n, Natural))

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\{x^{2 \cdot n} = \left(-x\right)^{2 \cdot n} \textrm{ if } 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	21, 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	19, 14
11	Literal
12	ExprTuple	13, 14
13	Operation	operator: 15 operand: 19
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19
17	Literal
18	ExprTuple	20, 21
19	Variable
20	Literal
21	Variable