Theorem nth_root_of_nth_power 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 nth_root_of_nth_power

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

Passed sanity check: nth_root_of_nth_power matches stored_expr

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

\forall_{n \in \mathbb{N}^+}~\left[\forall_{x~|~x \geq 0}~\left(\sqrt[\leftroot{-3}\uproot{3}n]{(x^{n})} = x\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: 32 body: 4
3	ExprTuple	32
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	32, 12
11	Lambda	parameter: 30 body: 14
12	Literal
13	ExprTuple	30
14	Conditional	value: 15 condition: 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 30
19	Literal
20	ExprTuple	22, 30
21	Operation	operator: 26 operands: 23
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	30, 32
28	Literal
29	ExprTuple	31, 32
30	Variable
31	Literal
32	Variable