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 And, Forall, Implies
from proveit.numbers import Natural

# build up the expression from sub-expressions
sub_expr1 = [n]
sub_expr2 = Forall(instance_param_or_params = [x_1_to_n], instance_expr = P__x_1_to_n)
expr = ExprTuple(And(Function(P, []), Forall(instance_param_or_params = sub_expr1, instance_expr = Implies(sub_expr2, Forall(instance_param_or_params = [x_1_to_np1], instance_expr = P__x_1_to_np1)).with_wrapping_at(2), domain = Natural)), Forall(instance_param_or_params = sub_expr1, instance_expr = sub_expr2, 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) \land \left[\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], \forall_{n \in \mathbb{N}}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n}}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\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: 3 operands: 4
2	Operation	operator: 25 operand: 8
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	8
6	Operation	operator: 32 operands: 9
7	Operation	operator: 25 operand: 12
8	Lambda	parameter: 43 body: 11
9	ExprTuple
10	ExprTuple	12
11	Conditional	value: 21 condition: 16
12	Lambda	parameter: 43 body: 14
13	ExprTuple	43
14	Conditional	value: 15 condition: 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	43, 23
21	Operation	operator: 25 operand: 27
22	Operation	operator: 25 operand: 28
23	Literal
24	ExprTuple	27
25	Literal
26	ExprTuple	28
27	Lambda	parameters: 31 body: 29
28	Lambda	parameters: 33 body: 30
29	Operation	operator: 32 operands: 31
30	Operation	operator: 32 operands: 33
31	ExprTuple	34
32	Variable
33	ExprTuple	35
34	ExprRange	lambda_map: 36 start_index: 44 end_index: 43
35	ExprRange	lambda_map: 36 start_index: 44 end_index: 37
36	Lambda	parameter: 45 body: 38
37	Operation	operator: 39 operands: 40
38	IndexedVar	variable: 41 index: 45
39	Literal
40	ExprTuple	43, 44
41	Variable
42	ExprTuple	45
43	Variable
44	Literal
45	Variable