Expression of type Forall

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

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

\forall_{x \in \mathbb{C}}~\left[\forall_{n \in \mathbb{N}}~\left(\left(-x\right)^{2 \cdot n} = x^{2 \cdot n}\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 31 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 17 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	31, 10
9	Lambda	parameter: 33 body: 12
10	Literal
11	ExprTuple	33
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	33, 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	31, 26
25	Operation	operator: 27 operand: 31
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31
29	Literal
30	ExprTuple	32, 33
31	Variable
32	Literal
33	Variable