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 ExprTuple, Function, P, 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
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Function(P, []), Forall(instance_param_or_params = [n], instance_expr = 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), domain = 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(P\left(\right), \forall_{n \in \mathbb{N}}~\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}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 25 operands: 3
2	Operation	operator: 18 operand: 5
3	ExprTuple
4	ExprTuple	5
5	Lambda	parameter: 36 body: 7
6	ExprTuple	36
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	36, 16
14	Operation	operator: 18 operand: 20
15	Operation	operator: 18 operand: 21
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	21
20	Lambda	parameters: 24 body: 22
21	Lambda	parameters: 26 body: 23
22	Operation	operator: 25 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	27
25	Variable
26	ExprTuple	28
27	ExprRange	lambda_map: 29 start_index: 37 end_index: 36
28	ExprRange	lambda_map: 29 start_index: 37 end_index: 30
29	Lambda	parameter: 38 body: 31
30	Operation	operator: 32 operands: 33
31	IndexedVar	variable: 34 index: 38
32	Literal
33	ExprTuple	36, 37
34	Variable
35	ExprTuple	38
36	Variable
37	Literal
38	Variable