Theorem int_exp_of_exp 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 int_exp_of_exp

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

Passed sanity check: int_exp_of_exp matches stored_expr

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

\forall_{n \in \mathbb{Z}}~\left[\forall_{a, b \in \mathbb{C}~|~a \neq 0}~\left((a^{b})^{n} = a^{b \cdot n}\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 41 body: 4
3	ExprTuple	41
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 27 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	41, 11
10	Lambda	parameters: 36 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22, 23
19	Operation	operator: 35 operands: 24
20	Operation	operator: 35 operands: 25
21	Operation	operator: 27 operands: 26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 29 operands: 30
24	ExprTuple	31, 41
25	ExprTuple	39, 32
26	ExprTuple	39, 33
27	Literal
28	ExprTuple	40, 33
29	Literal
30	ExprTuple	39, 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operands: 38
33	Literal
34	Literal
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	40, 41
39	Variable
40	Variable
41	Variable