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, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Exp, Mod, Mult, Neg, Real, e, frac, i, pi, two

# build up the expression from sub-expressions
expr = Lambda([x, r], Conditional(Equals(Exp(e, frac(Neg(Mult(two, pi, i, Mod(x, r))), r)), Exp(e, frac(Neg(Mult(two, pi, i, x)), r))), And(InSet(x, Real), InSet(r, 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(x, r\right) \mapsto \left\{\mathsf{e}^{\frac{-\left(2 \cdot \pi \cdot \mathsf{i} \cdot \left(x ~\textup{mod}~ r\right)\right)}{r}} = \mathsf{e}^{\frac{-\left(2 \cdot \pi \cdot \mathsf{i} \cdot x\right)}{r}} \textrm{ if } x \in \mathbb{R} ,  r \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: 40 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	19, 18
13	Literal
14	ExprTuple	19, 20
15	ExprTuple	41, 21
16	Literal
17	ExprTuple	42, 21
18	Operation	operator: 23 operands: 22
19	Literal
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 42
23	Literal
24	ExprTuple	26, 42
25	Operation	operator: 28 operand: 30
26	Operation	operator: 28 operand: 31
27	ExprTuple	30
28	Literal
29	ExprTuple	31
30	Operation	operator: 33 operands: 32
31	Operation	operator: 33 operands: 34
32	ExprTuple	36, 37, 38, 35
33	Literal
34	ExprTuple	36, 37, 38, 41
35	Operation	operator: 39 operands: 40
36	Literal
37	Literal
38	Literal
39	Literal
40	ExprTuple	41, 42
41	Variable
42	Variable