Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([r, theta], 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(r, \theta\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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