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(r, Exp(e, Mult(i, Add(theta, pi)))), Neg(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(r \cdot \mathsf{e}^{\mathsf{i} \cdot \left(\theta + \pi\right)}\right) = \left(-\left(r \cdot \mathsf{e}^{\mathsf{i} \cdot \theta}\right)\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	26, 40
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: 36 operands: 14
11	Operation	operator: 15 operand: 21
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	26, 20
15	Literal
16	ExprTuple	21
17	ExprTuple	26, 22
18	Literal
19	ExprTuple	40, 22
20	Operation	operator: 29 operands: 23
21	Operation	operator: 36 operands: 24
22	Literal
23	ExprTuple	32, 25
24	ExprTuple	26, 27
25	Operation	operator: 36 operands: 28
26	Variable
27	Operation	operator: 29 operands: 30
28	ExprTuple	39, 31
29	Literal
30	ExprTuple	32, 33
31	Operation	operator: 34 operands: 35
32	Literal
33	Operation	operator: 36 operands: 37
34	Literal
35	ExprTuple	40, 38
36	Literal
37	ExprTuple	39, 40
38	Literal
39	Literal
40	Variable