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 Equals, Forall, InSet, NotEquals
from proveit.numbers import Complex, Exp, Integer, Mult, zero

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a, b], instance_expr = Equals(Exp(Exp(a, b), n), Exp(a, Mult(b, n))), domain = Complex, condition = NotEquals(a, zero)), InSet(n, Integer))

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_{a, b \in \mathbb{C}~|~a \neq 0}~\left((a^{b})^{n} = a^{b \cdot n}\right) \textrm{ if } n \in \mathbb{Z}\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: 23 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	37, 7
6	Lambda	parameters: 32 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18, 19
15	Operation	operator: 31 operands: 20
16	Operation	operator: 31 operands: 21
17	Operation	operator: 23 operands: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 25 operands: 26
20	ExprTuple	27, 37
21	ExprTuple	35, 28
22	ExprTuple	35, 29
23	Literal
24	ExprTuple	36, 29
25	Literal
26	ExprTuple	35, 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operands: 34
29	Literal
30	Literal
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	36, 37
35	Variable
36	Variable
37	Variable