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, Lambda, 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(Lambda(P, Implies(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)).with_wrapping_at(1)))

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 \mapsto \left(\begin{array}{c} \begin{array}{l} \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]\right) \\  \Rightarrow \left[\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] \end{array} \end{array}\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: 36 body: 3
2	ExprTuple	36
3	Operation	operator: 21 operands: 4
4	ExprTuple	5, 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 29 operand: 12
7	Literal
8	ExprTuple	10, 11
9	ExprTuple	12
10	Operation	operator: 36 operands: 13
11	Operation	operator: 29 operand: 16
12	Lambda	parameter: 47 body: 15
13	ExprTuple
14	ExprTuple	16
15	Conditional	value: 25 condition: 20
16	Lambda	parameter: 47 body: 18
17	ExprTuple	47
18	Conditional	value: 19 condition: 20
19	Operation	operator: 21 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	47, 27
25	Operation	operator: 29 operand: 31
26	Operation	operator: 29 operand: 32
27	Literal
28	ExprTuple	31
29	Literal
30	ExprTuple	32
31	Lambda	parameters: 35 body: 33
32	Lambda	parameters: 37 body: 34
33	Operation	operator: 36 operands: 35
34	Operation	operator: 36 operands: 37
35	ExprTuple	38
36	Variable
37	ExprTuple	39
38	ExprRange	lambda_map: 40 start_index: 48 end_index: 47
39	ExprRange	lambda_map: 40 start_index: 48 end_index: 41
40	Lambda	parameter: 49 body: 42
41	Operation	operator: 43 operands: 44
42	IndexedVar	variable: 45 index: 49
43	Literal
44	ExprTuple	47, 48
45	Variable
46	ExprTuple	49
47	Variable
48	Literal
49	Variable