Theorem membership_unfolding of type Forall

from the theory of proveit.logic.sets.subtraction

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.subtraction import membership_unfolding

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

Passed sanity check: membership_unfolding matches stored_expr

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

\forall_{x, A, B~|~x \in \left(A - B\right)}~\left(\left(x \in A\right) \land \left(x \notin B\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	20, 21, 22
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 14 operands: 10
8	Literal
9	ExprTuple	11, 12
10	ExprTuple	20, 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Literal
15	ExprTuple	20, 21
16	Literal
17	ExprTuple	20, 22
18	Literal
19	ExprTuple	21, 22
20	Variable
21	Variable
22	Variable