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

# build up the expression from sub-expressions
expr = Lambda(theta, Conditional(NotEquals(Exp(e, Mult(i, theta)), one), And(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())

\theta \mapsto \left\{\mathsf{e}^{\mathsf{i} \cdot \theta} \neq 1 \textrm{ if } \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	parameter: 28 body: 2
1	ExprTuple	28
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: 13 operands: 14
10	Literal
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	Literal
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	28, 21
17	Literal
18	ExprTuple	22, 23
19	Literal
20	Operation	operator: 30 operands: 24
21	Literal
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	28, 29
27	Literal
28	Variable
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Literal