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, Lambda, P, Q, alpha
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
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([P, Q, alpha], 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)))

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(P, Q, \alpha\right) \mapsto \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)\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	30, 25, 28
3	Operation	operator: 23 operands: 4
4	ExprTuple	5, 28
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 10 operand: 14
9	Operation	operator: 12 operand: 15
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	15
14	Lambda	parameters: 22 body: 16
15	Lambda	parameters: 31 body: 17
16	Conditional	value: 18 condition: 19
17	Conditional	value: 20 condition: 21
18	Operation	operator: 30 operands: 22
19	Operation	operator: 25 operands: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 31
22	ExprTuple	26
23	Literal
24	ExprTuple	27, 28
25	Variable
26	ExprRange	lambda_map: 29 start_index: 36 end_index: 37
27	Operation	operator: 30 operands: 31
28	Variable
29	Lambda	parameter: 41 body: 32
30	Variable
31	ExprTuple	33
32	IndexedVar	variable: 34 index: 41
33	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
34	Variable
35	Lambda	parameter: 41 body: 38
36	Literal
37	Variable
38	IndexedVar	variable: 39 index: 41
39	Variable
40	ExprTuple	41
41	Variable