Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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