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)), Neg(n)), Exp(a, 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^{b \cdot n}\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: 42 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 26 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	42, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	40, 45
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	Operation	operator: 35 operands: 23
19	Operation	operator: 35 operands: 24
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 28 operands: 29
23	ExprTuple	30, 31
24	ExprTuple	40, 32
25	ExprTuple	40, 33
26	Literal
27	ExprTuple	45, 33
28	Literal
29	ExprTuple	40, 34
30	Operation	operator: 35 operands: 36
31	Operation	operator: 43 operand: 42
32	Operation	operator: 38 operands: 39
33	Literal
34	Literal
35	Literal
36	ExprTuple	40, 41
37	ExprTuple	42
38	Literal
39	ExprTuple	45, 42
40	Variable
41	Operation	operator: 43 operand: 45
42	Variable
43	Literal
44	ExprTuple	45
45	Variable