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, 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, Conditional(Forall(instance_param_or_params = [P, Q, alpha], 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)), InSet(n, NaturalPos))))

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