Expression of type ExprTuple

from the theory of proveit.logic.booleans.quantification.existence

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, alpha, n
from proveit.core_expr_types import P__x_1_to_n, Q__x_1_to_n, x_1_to_n
from proveit.logic import And, Boolean, Forall, Implies, InSet
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(And(InSet(n, NaturalPos), InSet(alpha, Boolean)), And(general_exists_Py_st_Qy, Forall(instance_param_or_params = [x_1_to_n], instance_expr = Implies(P__x_1_to_n, alpha), condition = Q__x_1_to_n)))

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(\left(n \in \mathbb{N}^+\right) \land \left(\alpha \in \mathbb{B}\right), \left[\exists_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right] \land \left[\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~\left(P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \Rightarrow \alpha\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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 11 operands: 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operand: 19
9	Operation	operator: 15 operand: 20
10	ExprTuple	42, 17
11	Literal
12	ExprTuple	33, 18
13	Literal
14	ExprTuple	19
15	Literal
16	ExprTuple	20
17	Literal
18	Literal
19	Lambda	parameters: 27 body: 21
20	Lambda	parameters: 36 body: 22
21	Conditional	value: 23 condition: 24
22	Conditional	value: 25 condition: 26
23	Operation	operator: 35 operands: 27
24	Operation	operator: 30 operands: 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 36
27	ExprTuple	31
28	Literal
29	ExprTuple	32, 33
30	Variable
31	ExprRange	lambda_map: 34 start_index: 41 end_index: 42
32	Operation	operator: 35 operands: 36
33	Variable
34	Lambda	parameter: 46 body: 37
35	Variable
36	ExprTuple	38
37	IndexedVar	variable: 39 index: 46
38	ExprRange	lambda_map: 40 start_index: 41 end_index: 42
39	Variable
40	Lambda	parameter: 46 body: 43
41	Literal
42	Variable
43	IndexedVar	variable: 44 index: 46
44	Variable
45	ExprTuple	46
46	Variable