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, m, 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, m, n], Conditional(Equals(Exp(Exp(a, m), n), Exp(a, Mult(m, n))), And(InSet(a, Complex), InSet(m, NaturalPos), 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, m, n\right) \mapsto \left\{(a^{m})^{n} = a^{m \cdot n} \textrm{ if } a \in \mathbb{C} ,  m \in \mathbb{N}^+ ,  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	29, 30, 31
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: 25 operands: 15
11	Operation	operator: 25 operands: 16
12	Operation	operator: 19 operands: 17
13	Operation	operator: 19 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	21, 31
16	ExprTuple	29, 22
17	ExprTuple	29, 23
18	ExprTuple	30, 24
19	Literal
20	ExprTuple	31, 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	Literal
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Variable
31	Variable