Expression of type Lambda

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, Lambda, r, theta
from proveit.logic import And, InSet, NotEquals, NotInSet
from proveit.numbers import Exp, Integer, Mult, Real, RealPos, e, frac, i, pi, two

# build up the expression from sub-expressions
expr = Lambda([r, theta], Conditional(NotEquals(Mult(r, Exp(e, Mult(i, theta))), r), And(InSet(r, RealPos), InSet(theta, Real), NotInSet(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(r, \theta\right) \mapsto \left\{\left(r \cdot \mathsf{e}^{\mathsf{i} \cdot \theta}\right) \neq r \textrm{ if } r \in \mathbb{R}^+ ,  \theta \in \mathbb{R} ,  \frac{\theta}{2 \cdot \pi} \notin \mathbb{Z}\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	20, 36
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 20
7	Literal
8	ExprTuple	10, 11, 12
9	Operation	operator: 33 operands: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	ExprTuple	20, 19
14	ExprTuple	20, 21
15	Literal
16	ExprTuple	36, 22
17	Literal
18	ExprTuple	23, 24
19	Operation	operator: 25 operands: 26
20	Variable
21	Literal
22	Literal
23	Operation	operator: 27 operands: 28
24	Literal
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	36, 31
29	Literal
30	Operation	operator: 33 operands: 32
31	Operation	operator: 33 operands: 34
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37, 38
35	Literal
36	Variable
37	Literal
38	Literal