Theorem int_exp_of_neg_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_neg_exp

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

Passed sanity check: int_exp_of_neg_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^{-\left(b \cdot n\right)}\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: 47 body: 4
3	ExprTuple	47
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 28 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	47, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	39, 46
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23, 24
20	Operation	operator: 36 operands: 25
21	Operation	operator: 36 operands: 26
22	Operation	operator: 28 operands: 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 30 operands: 31
25	ExprTuple	32, 47
26	ExprTuple	39, 33
27	ExprTuple	39, 34
28	Literal
29	ExprTuple	46, 34
30	Literal
31	ExprTuple	39, 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 42 operand: 41
34	Literal
35	Literal
36	Literal
37	ExprTuple	39, 40
38	ExprTuple	41
39	Variable
40	Operation	operator: 42 operand: 46
41	Operation	operator: 44 operands: 45
42	Literal
43	ExprTuple	46
44	Literal
45	ExprTuple	46, 47
46	Variable
47	Variable