Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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