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, theta
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Exp, Mult, Neg, Real, e, i, pi

# build up the expression from sub-expressions
expr = Lambda(theta, Conditional(Equals(Exp(e, Mult(i, Add(theta, pi))), Neg(Exp(e, Mult(i, theta)))), 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())

\theta \mapsto \left\{\mathsf{e}^{\mathsf{i} \cdot \left(\theta + \pi\right)} = \left(-\mathsf{e}^{\mathsf{i} \cdot \theta}\right) \textrm{ if } \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	parameter: 29 body: 2
1	ExprTuple	29
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	29, 11
9	Operation	operator: 18 operands: 12
10	Operation	operator: 13 operand: 16
11	Literal
12	ExprTuple	21, 15
13	Literal
14	ExprTuple	16
15	Operation	operator: 25 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	28, 20
18	Literal
19	ExprTuple	21, 22
20	Operation	operator: 23 operands: 24
21	Literal
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	29, 27
25	Literal
26	ExprTuple	28, 29
27	Literal
28	Literal
29	Variable