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 And, Equals, InSet
from proveit.numbers import Complex, Exp, Mult, NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b, n], Conditional(Equals(Exp(Mult(a, b), n), Mult(Exp(a, n), Exp(b, n))), And(InSet(a, Complex), InSet(b, Complex), InSet(n, NaturalPos)))))

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(a, b, n\right) \mapsto \left\{\left(a \cdot b\right)^{n} = \left(a^{n} \cdot b^{n}\right) \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  n \in \mathbb{N}^+\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: 2 body: 3
2	ExprTuple	31, 32, 33
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14
10	Operation	operator: 29 operands: 15
11	Operation	operator: 26 operands: 16
12	Operation	operator: 19 operands: 17
13	Operation	operator: 19 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	21, 33
16	ExprTuple	22, 23
17	ExprTuple	31, 24
18	ExprTuple	32, 24
19	Literal
20	ExprTuple	33, 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 29 operands: 28
23	Operation	operator: 29 operands: 30
24	Literal
25	Literal
26	Literal
27	ExprTuple	31, 32
28	ExprTuple	31, 33
29	Literal
30	ExprTuple	32, 33
31	Variable
32	Variable
33	Variable