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
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(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[\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], \alpha\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, 24
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operand: 11
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11
10	Lambda	parameters: 18 body: 12
11	Lambda	parameters: 27 body: 13
12	Conditional	value: 14 condition: 15
13	Conditional	value: 16 condition: 17
14	Operation	operator: 26 operands: 18
15	Operation	operator: 21 operands: 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 27
18	ExprTuple	22
19	Literal
20	ExprTuple	23, 24
21	Variable
22	ExprRange	lambda_map: 25 start_index: 32 end_index: 33
23	Operation	operator: 26 operands: 27
24	Variable
25	Lambda	parameter: 37 body: 28
26	Variable
27	ExprTuple	29
28	IndexedVar	variable: 30 index: 37
29	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
30	Variable
31	Lambda	parameter: 37 body: 34
32	Literal
33	Variable
34	IndexedVar	variable: 35 index: 37
35	Variable
36	ExprTuple	37
37	Variable