Theorem neg_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 neg_int_exp_of_neg_exp

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

Passed sanity check: neg_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^{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: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 43 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 27 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	43, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	41, 46
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: 36 operands: 24
20	Operation	operator: 36 operands: 25
21	Operation	operator: 27 operands: 26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 29 operands: 30
24	ExprTuple	31, 32
25	ExprTuple	41, 33
26	ExprTuple	41, 34
27	Literal
28	ExprTuple	46, 34
29	Literal
30	ExprTuple	41, 35
31	Operation	operator: 36 operands: 37
32	Operation	operator: 44 operand: 43
33	Operation	operator: 39 operands: 40
34	Literal
35	Literal
36	Literal
37	ExprTuple	41, 42
38	ExprTuple	43
39	Literal
40	ExprTuple	46, 43
41	Variable
42	Operation	operator: 44 operand: 46
43	Variable
44	Literal
45	ExprTuple	46
46	Variable