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 Exp, NaturalPos, frac, greater_eq, one, zero

# build up the expression from sub-expressions
expr = ExprTuple(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())

\left(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..\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: 31 body: 3
2	ExprTuple	31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	31, 11
10	Lambda	parameter: 29 body: 13
11	Literal
12	ExprTuple	29
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 29
18	Literal
19	ExprTuple	21, 29
20	Operation	operator: 25 operands: 22
21	Literal
22	ExprTuple	23, 24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	29, 31
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Literal
31	Variable