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, Forall, InSet
from proveit.numbers import Complex, Exp, Mult, Natural, Neg, two

# build up the expression from sub-expressions
sub_expr1 = Mult(two, n)
expr = ExprTuple(Lambda(x, Conditional(Forall(instance_param_or_params = [n], instance_expr = Equals(Exp(Neg(x), sub_expr1), Exp(x, sub_expr1)), domain = Natural), InSet(x, Complex))))

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