Theorem in_superset_if_in_comprehension of type Forall

from the theory of proveit.logic.sets.comprehension

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.logic.sets.comprehension import in_superset_if_in_comprehension

# check that the built expression is the same as the stored expression
assert in_superset_if_in_comprehension.expr == stored_expr
assert in_superset_if_in_comprehension.expr._style_id == stored_expr._style_id
print("Passed sanity check: in_superset_if_in_comprehension matches stored_expr")

Passed sanity check: in_superset_if_in_comprehension matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{S, Q}~\left[\forall_{x \in \left\{y~|~Q\left(y\right)\right\}_{y \in S}}~\left(x \in S\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 5 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	29, 27
4	Operation	operator: 5 operand: 7
5	Literal
6	ExprTuple	7
7	Lambda	parameter: 14 body: 9
8	ExprTuple	14
9	Conditional	value: 10 condition: 11
10	Operation	operator: 25 operands: 12
11	Operation	operator: 25 operands: 13
12	ExprTuple	14, 29
13	ExprTuple	14, 15
14	Variable
15	Operation	operator: 16 operand: 18
16	Literal
17	ExprTuple	18
18	Lambda	parameter: 30 body: 19
19	Conditional	value: 30 condition: 20
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	23, 24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 27 operand: 30
25	Literal
26	ExprTuple	30, 29
27	Variable
28	ExprTuple	30
29	Variable
30	Variable