Theorem unit_length_complex_polar_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 unit_length_complex_polar_negation

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

Passed sanity check: unit_length_complex_polar_negation matches stored_expr

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

\forall_{\theta \in \mathbb{R}}~\left(\mathsf{e}^{\mathsf{i} \cdot \left(\theta + \pi\right)} = \left(-\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	parameter: 32 body: 5
4	ExprTuple	32
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	32, 14
12	Operation	operator: 21 operands: 15
13	Operation	operator: 16 operand: 19
14	Literal
15	ExprTuple	24, 18
16	Literal
17	ExprTuple	19
18	Operation	operator: 28 operands: 20
19	Operation	operator: 21 operands: 22
20	ExprTuple	31, 23
21	Literal
22	ExprTuple	24, 25
23	Operation	operator: 26 operands: 27
24	Literal
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	32, 30
28	Literal
29	ExprTuple	31, 32
30	Literal
31	Literal
32	Variable