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, 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, b), 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: 40 body: 3
2	ExprTuple	40
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 26 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	40, 10
9	Lambda	parameters: 35 body: 11
10	Literal
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: 34 operands: 23
19	Operation	operator: 34 operands: 24
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 28 operands: 29
23	ExprTuple	30, 40
24	ExprTuple	38, 31
25	ExprTuple	38, 32
26	Literal
27	ExprTuple	39, 32
28	Literal
29	ExprTuple	38, 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 36 operands: 37
32	Literal
33	Literal
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	39, 40
38	Variable
39	Variable
40	Variable