Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 29 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 15 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	29, 8
7	Lambda	parameter: 31 body: 10
8	Literal
9	ExprTuple	31
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	31, 19
17	Operation	operator: 21 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	29, 24
23	Operation	operator: 25 operand: 29
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	29
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Literal
31	Variable