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, NotEquals
from proveit.numbers import Complex, Exp, NaturalPos, frac, subtract, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, m, n], Conditional(Equals(frac(Exp(a, m), Exp(a, n)), Exp(a, subtract(m, n))), And(InSet(a, Complex), InSet(m, NaturalPos), InSet(n, NaturalPos), NotEquals(a, zero)))))

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\{\frac{a^{m}}{a^{n}} = a^{m - n} \textrm{ if } a \in \mathbb{C} ,  m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+ ,  a \neq 0\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	36, 37, 41
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, 15
10	Operation	operator: 16 operands: 17
11	Operation	operator: 32 operands: 18
12	Operation	operator: 21 operands: 19
13	Operation	operator: 21 operands: 20
14	Operation	operator: 21 operands: 22
15	Operation	operator: 23 operands: 24
16	Literal
17	ExprTuple	25, 26
18	ExprTuple	36, 27
19	ExprTuple	36, 28
20	ExprTuple	37, 29
21	Literal
22	ExprTuple	41, 29
23	Literal
24	ExprTuple	36, 30
25	Operation	operator: 32 operands: 31
26	Operation	operator: 32 operands: 33
27	Operation	operator: 34 operands: 35
28	Literal
29	Literal
30	Literal
31	ExprTuple	36, 37
32	Literal
33	ExprTuple	36, 41
34	Literal
35	ExprTuple	37, 38
36	Variable
37	Variable
38	Operation	operator: 39 operand: 41
39	Literal
40	ExprTuple	41
41	Variable