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, Forall, InSet
from proveit.numbers import Complex, Exp, Mult, Natural, Neg, two

# build up the expression from sub-expressions
sub_expr1 = Mult(two, n)
expr = Conditional(Forall(instance_param_or_params = [n], instance_expr = Equals(Exp(Neg(x), sub_expr1), Exp(x, sub_expr1)), domain = Natural), InSet(x, Complex))

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\{\forall_{n \in \mathbb{N}}~\left(\left(-x\right)^{2 \cdot n} = x^{2 \cdot n}\right) \textrm{ if } x \in \mathbb{C}\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 operand: 6
2	Operation	operator: 14 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	28, 7
6	Lambda	parameter: 30 body: 9
7	Literal
8	ExprTuple	30
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	30, 18
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	28, 23
22	Operation	operator: 24 operand: 28
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Literal
30	Variable