Expression of type ExprTuple

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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, r], Conditional(Equals(Exp(e, frac(Mult(two, pi, i, Mod(x, r)), r)), Exp(e, frac(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(\left(x, r\right) \mapsto \left\{\mathsf{e}^{\frac{2 \cdot \pi \cdot \mathsf{i} \cdot \left(x ~\textup{mod}~ r\right)}{r}} = \mathsf{e}^{\frac{2 \cdot \pi \cdot \mathsf{i} \cdot x}{r}} \textrm{ if } x \in \mathbb{R} ,  r \in \mathbb{R}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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