Theorem unfold_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 unfold_basic_comprehension

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

Passed sanity check: unfold_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}~\left[\forall_{x \in \left\{y~|~Q\left(y\right)\right\}_{y \in S}}~\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: 5 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	32, 30
4	Operation	operator: 5 operand: 7
5	Literal
6	ExprTuple	7
7	Lambda	parameter: 20 body: 8
8	Conditional	value: 9 condition: 10
9	Operation	operator: 24 operands: 11
10	Operation	operator: 28 operands: 12
11	ExprTuple	13, 14
12	ExprTuple	20, 15
13	Operation	operator: 28 operands: 16
14	Operation	operator: 30 operand: 20
15	Operation	operator: 18 operand: 21
16	ExprTuple	20, 32
17	ExprTuple	20
18	Literal
19	ExprTuple	21
20	Variable
21	Lambda	parameter: 33 body: 22
22	Conditional	value: 33 condition: 23
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Operation	operator: 28 operands: 29
27	Operation	operator: 30 operand: 33
28	Literal
29	ExprTuple	33, 32
30	Variable
31	ExprTuple	33
32	Variable
33	Variable