Theorem basic_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 basic_comprehension

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

Passed sanity check: basic_comprehension matches stored_expr

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

\forall_{S, Q, x}~\left(\left(x \in \left\{y~|~Q\left(y\right)\right\}_{y \in S}\right) = \left(\left(x \in S\right) \land Q\left(x\right)\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	31, 29, 20
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 27 operands: 10
9	Operation	operator: 23 operands: 11
10	ExprTuple	20, 12
11	ExprTuple	13, 14
12	Operation	operator: 15 operand: 19
13	Operation	operator: 27 operands: 17
14	Operation	operator: 29 operand: 20
15	Literal
16	ExprTuple	19
17	ExprTuple	20, 31
18	ExprTuple	20
19	Lambda	parameter: 32 body: 21
20	Variable
21	Conditional	value: 32 condition: 22
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operand: 32
27	Literal
28	ExprTuple	32, 31
29	Variable
30	ExprTuple	32
31	Variable
32	Variable