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 Exp, NaturalPos, frac, greater_eq, one, zero

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(Exp(Exp(x, n), frac(one, n)), x), condition = greater_eq(x, zero)), 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())

n \mapsto \left\{\forall_{x~|~x \geq 0}~\left(\sqrt[\leftroot{-3}\uproot{3}n]{(x^{n})} = x\right) \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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