Expression of type Conditional

from the theory of proveit.numbers.number_sets.complex_numbers

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, r, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Exp, Mod, Mult, Neg, Real, e, frac, i, pi, two

# build up the expression from sub-expressions
expr = Conditional(Equals(Exp(e, frac(Neg(Mult(two, pi, i, Mod(x, r))), r)), Exp(e, frac(Neg(Mult(two, pi, i, x)), r))), And(InSet(x, Real), InSet(r, Real)))

expr:

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

Passed sanity check: expr matches stored_expr

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

\left\{\mathsf{e}^{\frac{-\left(2 \cdot \pi \cdot \mathsf{i} \cdot \left(x ~\textup{mod}~ r\right)\right)}{r}} = \mathsf{e}^{\frac{-\left(2 \cdot \pi \cdot \mathsf{i} \cdot x\right)}{r}} \textrm{ if } x \in \mathbb{R} ,  r \in \mathbb{R}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 12 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	18, 17
12	Literal
13	ExprTuple	18, 19
14	ExprTuple	40, 20
15	Literal
16	ExprTuple	41, 20
17	Operation	operator: 22 operands: 21
18	Literal
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24, 41
22	Literal
23	ExprTuple	25, 41
24	Operation	operator: 27 operand: 29
25	Operation	operator: 27 operand: 30
26	ExprTuple	29
27	Literal
28	ExprTuple	30
29	Operation	operator: 32 operands: 31
30	Operation	operator: 32 operands: 33
31	ExprTuple	35, 36, 37, 34
32	Literal
33	ExprTuple	35, 36, 37, 40
34	Operation	operator: 38 operands: 39
35	Literal
36	Literal
37	Literal
38	Literal
39	ExprTuple	40, 41
40	Variable
41	Variable