Expression of type ExprTuple

from the theory of proveit.logic.booleans.quantification.universality

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
from proveit.core_expr_types import P__x_1_to_n, P__x_1_to_np1, x_1_to_n, x_1_to_np1
from proveit.logic import Forall, Implies, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Implies(Forall(instance_param_or_params = [x_1_to_n], instance_expr = P__x_1_to_n), Forall(instance_param_or_params = [x_1_to_np1], instance_expr = P__x_1_to_np1)).with_wrapping_at(2), InSet(n, Natural))))

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\{\begin{array}{c} \begin{array}{l} \left[\forall_{x_{1}, x_{2}, \ldots, x_{n}}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \Rightarrow  \\ \left[\forall_{x_{1}, x_{2}, \ldots, x_{n + 1}}~P\left(x_{1}, x_{2}, \ldots, x_{n + 1}\right)\right] \end{array} \end{array} \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: 32 body: 3
2	ExprTuple	32
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	32, 12
10	Operation	operator: 14 operand: 16
11	Operation	operator: 14 operand: 17
12	Literal
13	ExprTuple	16
14	Literal
15	ExprTuple	17
16	Lambda	parameters: 20 body: 18
17	Lambda	parameters: 22 body: 19
18	Operation	operator: 21 operands: 20
19	Operation	operator: 21 operands: 22
20	ExprTuple	23
21	Variable
22	ExprTuple	24
23	ExprRange	lambda_map: 25 start_index: 33 end_index: 32
24	ExprRange	lambda_map: 25 start_index: 33 end_index: 26
25	Lambda	parameter: 34 body: 27
26	Operation	operator: 28 operands: 29
27	IndexedVar	variable: 30 index: 34
28	Literal
29	ExprTuple	32, 33
30	Variable
31	ExprTuple	34
32	Variable
33	Literal
34	Variable