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 Forall, Implies
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy

# build up the expression from sub-expressions
expr = ExprTuple(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(\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), \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)

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