Theorem real_power_of_product of type Forall

from the theory of proveit.numbers.exponentiation

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.numbers.exponentiation import real_power_of_product

# check that the built expression is the same as the stored expression
assert real_power_of_product.expr == stored_expr
assert real_power_of_product.expr._style_id == stored_expr._style_id
print("Passed sanity check: real_power_of_product matches stored_expr")

Passed sanity check: real_power_of_product matches stored_expr

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

\forall_{a \in \mathbb{C}, b \in \mathbb{C}, c \in \mathbb{R}~|~a \neq 0, b \neq 0}~\left(\left(a \cdot b\right)^{c} = \left(a^{c} \cdot b^{c}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	39, 40, 41
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16, 17, 18
12	Operation	operator: 37 operands: 19
13	Operation	operator: 34 operands: 20
14	Operation	operator: 23 operands: 21
15	Operation	operator: 23 operands: 22
16	Operation	operator: 23 operands: 24
17	Operation	operator: 26 operands: 25
18	Operation	operator: 26 operands: 27
19	ExprTuple	28, 41
20	ExprTuple	29, 30
21	ExprTuple	39, 31
22	ExprTuple	40, 31
23	Literal
24	ExprTuple	41, 32
25	ExprTuple	39, 33
26	Literal
27	ExprTuple	40, 33
28	Operation	operator: 34 operands: 35
29	Operation	operator: 37 operands: 36
30	Operation	operator: 37 operands: 38
31	Literal
32	Literal
33	Literal
34	Literal
35	ExprTuple	39, 40
36	ExprTuple	39, 41
37	Literal
38	ExprTuple	40, 41
39	Variable
40	Variable
41	Variable