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 Conditional, ExprTuple, Lambda, P, Q, 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(Lambda([n, alpha], Conditional(Forall(instance_param_or_params = [P, Q], instance_expr = Implies(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)), alpha)), And(InSet(n, NaturalPos), InSet(alpha, Boolean)))))

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, \alpha\right) \mapsto \left\{\forall_{P, Q}~\left(\left(\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) \Rightarrow \alpha\right) \textrm{ if } n \in \mathbb{N}^+ ,  \alpha \in \mathbb{B}\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	parameters: 2 body: 3
2	ExprTuple	51, 42
3	Conditional	value: 4 condition: 5
4	Operation	operator: 26 operand: 8
5	Operation	operator: 20 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 11 body: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	44, 39
12	Operation	operator: 37 operands: 16
13	ExprTuple	51, 17
14	Literal
15	ExprTuple	42, 18
16	ExprTuple	19, 42
17	Literal
18	Literal
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22, 23
22	Operation	operator: 24 operand: 28
23	Operation	operator: 26 operand: 29
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	29
28	Lambda	parameters: 36 body: 30
29	Lambda	parameters: 45 body: 31
30	Conditional	value: 32 condition: 33
31	Conditional	value: 34 condition: 35
32	Operation	operator: 44 operands: 36
33	Operation	operator: 39 operands: 36
34	Operation	operator: 37 operands: 38
35	Operation	operator: 39 operands: 45
36	ExprTuple	40
37	Literal
38	ExprTuple	41, 42
39	Variable
40	ExprRange	lambda_map: 43 start_index: 50 end_index: 51
41	Operation	operator: 44 operands: 45
42	Variable
43	Lambda	parameter: 55 body: 46
44	Variable
45	ExprTuple	47
46	IndexedVar	variable: 48 index: 55
47	ExprRange	lambda_map: 49 start_index: 50 end_index: 51
48	Variable
49	Lambda	parameter: 55 body: 52
50	Literal
51	Variable
52	IndexedVar	variable: 53 index: 55
53	Variable
54	ExprTuple	55
55	Variable