Expression of type ExprTuple

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, ExprTuple, Lambda, a, b, n
from proveit.logic import Equals, Forall, InSet, NotEquals
from proveit.numbers import Complex, Exp, Integer, Mult, Neg, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [a, b], instance_expr = Equals(Exp(Exp(a, Neg(b)), n), Exp(a, Neg(Mult(b, n)))), domain = Complex, condition = NotEquals(a, zero)), InSet(n, 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(n \mapsto \left\{\forall_{a, b \in \mathbb{C}~|~a \neq 0}~\left((a^{-b})^{n} = a^{-\left(b \cdot n\right)}\right) \textrm{ if } n \in \mathbb{Z}\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	parameter: 46 body: 3
2	ExprTuple	46
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 27 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	46, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	38, 45
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22, 23
19	Operation	operator: 35 operands: 24
20	Operation	operator: 35 operands: 25
21	Operation	operator: 27 operands: 26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 29 operands: 30
24	ExprTuple	31, 46
25	ExprTuple	38, 32
26	ExprTuple	38, 33
27	Literal
28	ExprTuple	45, 33
29	Literal
30	ExprTuple	38, 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 41 operand: 40
33	Literal
34	Literal
35	Literal
36	ExprTuple	38, 39
37	ExprTuple	40
38	Variable
39	Operation	operator: 41 operand: 45
40	Operation	operator: 43 operands: 44
41	Literal
42	ExprTuple	45
43	Literal
44	ExprTuple	45, 46
45	Variable
46	Variable