Theorem exp_2pi_i_x 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 exp_2pi_i_x

# check that the built expression is the same as the stored expression
assert exp_2pi_i_x.expr == stored_expr
assert exp_2pi_i_x.expr._style_id == stored_expr._style_id
print("Passed sanity check: exp_2pi_i_x matches stored_expr")

Passed sanity check: exp_2pi_i_x matches stored_expr

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

\forall_{x, r \in \mathbb{R}}~\left(\mathsf{e}^{\frac{2 \cdot \pi \cdot \mathsf{i} \cdot \left(x ~\textup{mod}~ r\right)}{r}} = \mathsf{e}^{\frac{2 \cdot \pi \cdot \mathsf{i} \cdot x}{r}}\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: 38 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 19 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	22, 21
16	Literal
17	ExprTuple	22, 23
18	ExprTuple	39, 24
19	Literal
20	ExprTuple	40, 24
21	Operation	operator: 26 operands: 25
22	Literal
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28, 40
26	Literal
27	ExprTuple	29, 40
28	Operation	operator: 31 operands: 30
29	Operation	operator: 31 operands: 32
30	ExprTuple	34, 35, 36, 33
31	Literal
32	ExprTuple	34, 35, 36, 39
33	Operation	operator: 37 operands: 38
34	Literal
35	Literal
36	Literal
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Variable