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
from proveit.logic.booleans.quantification import general_exists_in_A_Px_st_Qx, general_exists_in_B_Py_st_Qy

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

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_{x_{1}, x_{2}, \ldots, x_{n} \in A~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right), \exists_{y_{1}, y_{2}, \ldots, y_{n} \in B~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\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: 4 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Lambda	parameters: 23 body: 8
7	Lambda	parameters: 26 body: 9
8	Conditional	value: 10 condition: 11
9	Conditional	value: 12 condition: 13
10	Operation	operator: 15 operands: 23
11	Operation	operator: 16 operands: 14
12	Operation	operator: 15 operands: 26
13	Operation	operator: 16 operands: 17
14	ExprTuple	18, 19
15	Variable
16	Literal
17	ExprTuple	20, 21
18	ExprRange	lambda_map: 22 start_index: 36 end_index: 37
19	Operation	operator: 25 operands: 23
20	ExprRange	lambda_map: 24 start_index: 36 end_index: 37
21	Operation	operator: 25 operands: 26
22	Lambda	parameter: 45 body: 27
23	ExprTuple	28
24	Lambda	parameter: 45 body: 29
25	Variable
26	ExprTuple	30
27	Operation	operator: 33 operands: 31
28	ExprRange	lambda_map: 32 start_index: 36 end_index: 37
29	Operation	operator: 33 operands: 34
30	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
31	ExprTuple	39, 38
32	Lambda	parameter: 45 body: 39
33	Literal
34	ExprTuple	41, 40
35	Lambda	parameter: 45 body: 41
36	Literal
37	Variable
38	Variable
39	IndexedVar	variable: 42 index: 45
40	Variable
41	IndexedVar	variable: 43 index: 45
42	Variable
43	Variable
44	ExprTuple	45
45	Variable