Expression of type Conditional

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, 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 = 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\{\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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