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, n, x
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, Mult, Natural, Neg, two

# build up the expression from sub-expressions
sub_expr1 = Mult(two, n)
expr = ExprTuple(Lambda(n, Conditional(Equals(Exp(x, sub_expr1), Exp(Neg(x), sub_expr1)), InSet(n, Natural))))

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\{x^{2 \cdot n} = \left(-x\right)^{2 \cdot n} \textrm{ if } 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	parameter: 24 body: 3
2	ExprTuple	24
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	24, 12
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	22, 17
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 18 operand: 22
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Literal
24	Variable