Expression of type ExprTuple

from the theory of proveit.numbers.exponentiation

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 Exp, Integer, Mult, Real, e, frac, i, pi, two

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([r, theta], Conditional(Equals(Mult(r, Exp(e, Mult(i, theta))), r), And(InSet(r, Real), InSet(theta, Real), InSet(frac(theta, Mult(two, pi)), Integer)))))

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 \theta}\right) = r \textrm{ if } r \in \mathbb{R} ,  \theta \in \mathbb{R} ,  \frac{\theta}{2 \cdot \pi} \in \mathbb{Z}\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	20, 35
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 20
8	Literal
9	ExprTuple	11, 12, 13
10	Operation	operator: 32 operands: 14
11	Operation	operator: 17 operands: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	20, 19
15	ExprTuple	20, 21
16	ExprTuple	35, 21
17	Literal
18	ExprTuple	22, 23
19	Operation	operator: 24 operands: 25
20	Variable
21	Literal
22	Operation	operator: 26 operands: 27
23	Literal
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	35, 30
28	Literal
29	Operation	operator: 32 operands: 31
30	Operation	operator: 32 operands: 33
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36, 37
34	Literal
35	Variable
36	Literal
37	Literal