Theorem complex_polar_radius_negation of type Forall

from the theory of proveit.numbers.number_sets.complex_numbers

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.number_sets.complex_numbers import complex_polar_radius_negation

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

Passed sanity check: complex_polar_radius_negation matches stored_expr

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

\forall_{r, \theta \in \mathbb{R}}~\left(\left(\left(-r\right) \cdot \mathsf{e}^{\mathsf{i} \cdot \left(\theta + \pi\right)}\right) = \left(r \cdot \mathsf{e}^{\mathsf{i} \cdot \theta}\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	30, 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
12	Operation	operator: 35 operands: 16
13	Operation	operator: 35 operands: 17
14	Operation	operator: 19 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprTuple	21, 22
17	ExprTuple	30, 23
18	ExprTuple	30, 24
19	Literal
20	ExprTuple	41, 24
21	Operation	operator: 25 operand: 30
22	Operation	operator: 28 operands: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	Literal
26	ExprTuple	30
27	ExprTuple	32, 31
28	Literal
29	ExprTuple	32, 33
30	Variable
31	Operation	operator: 35 operands: 34
32	Literal
33	Operation	operator: 35 operands: 36
34	ExprTuple	38, 37
35	Literal
36	ExprTuple	38, 41
37	Operation	operator: 39 operands: 40
38	Literal
39	Literal
40	ExprTuple	41, 42
41	Variable
42	Literal