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, theta
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Exp, Mult, Neg, Real, e, i, pi

# build up the expression from sub-expressions
expr = Conditional(Equals(Mult(Neg(r), Exp(e, Mult(i, Add(theta, pi)))), Mult(r, Exp(e, Mult(i, theta)))), And(InSet(r, Real), InSet(theta, 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\{\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) \textrm{ if } r \in \mathbb{R} ,  \theta \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: 30 operands: 11
8	Operation	operator: 30 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	16, 17
12	ExprTuple	25, 18
13	ExprTuple	25, 19
14	Literal
15	ExprTuple	36, 19
16	Operation	operator: 20 operand: 25
17	Operation	operator: 23 operands: 22
18	Operation	operator: 23 operands: 24
19	Literal
20	Literal
21	ExprTuple	25
22	ExprTuple	27, 26
23	Literal
24	ExprTuple	27, 28
25	Variable
26	Operation	operator: 30 operands: 29
27	Literal
28	Operation	operator: 30 operands: 31
29	ExprTuple	33, 32
30	Literal
31	ExprTuple	33, 36
32	Operation	operator: 34 operands: 35
33	Literal
34	Literal
35	ExprTuple	36, 37
36	Variable
37	Literal