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 ComplexNonZero, Exp, NaturalPos, Neg, frac

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b, n], Conditional(Equals(Exp(frac(a, b), Neg(n)), frac(Exp(b, n), Exp(a, n))), And(InSet(a, ComplexNonZero), InSet(b, ComplexNonZero), 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(\frac{a}{b}\right)^{-n} = \frac{b^{n}}{a^{n}} \textrm{ if } a \in \mathbb{C}^{\neq 0} ,  b \in \mathbb{C}^{\neq 0} ,  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	35, 34, 36
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: 32 operands: 15
11	Operation	operator: 27 operands: 16
12	Operation	operator: 19 operands: 17
13	Operation	operator: 19 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	21, 22
16	ExprTuple	23, 24
17	ExprTuple	35, 25
18	ExprTuple	34, 25
19	Literal
20	ExprTuple	36, 26
21	Operation	operator: 27 operands: 28
22	Operation	operator: 29 operand: 36
23	Operation	operator: 32 operands: 31
24	Operation	operator: 32 operands: 33
25	Literal
26	Literal
27	Literal
28	ExprTuple	35, 34
29	Literal
30	ExprTuple	36
31	ExprTuple	34, 36
32	Literal
33	ExprTuple	35, 36
34	Variable
35	Variable
36	Variable